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.

A Bulk-Flow Analysis of Multiple-Pocket Gas Damper Seals

1999 ◽  
Vol 121 (2) ◽  
pp. 355-363 ◽  
Author(s):  
J. Li ◽  
L. San Andre´s ◽  
J. Vance
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Current Model ◽  
Flow Analysis ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Turbulent Shear ◽  
Dynamic Force ◽  
Gas Damper ◽  
Single Cavity

A bulk-flow model for calculation of the dynamic force characteristics in a single cavity, multiple-pocket gas damper seal is presented. Flow turbulence is accounted for by using turbulent shear stress parameters and Moody’s friction factors in the circumferential momentum equation. Zeroth-order-equations describe the isothermal flow field for a centered seal, and first-order equations govern the perturbed flow for small amplitude rotor lateral motions. Comparisons to limited measurements from a four-pocket gas damper seal show the current model to predict well the mass flow rate and the direct damping coefficient. For a reference two-bladed teeth-on-stator labyrinth seal, the current model predicts similar rotordynamic coefficients when compared to results from a two control volume, bulk-flow model. Force coefficients from a reference single-cavity, four pocket gas damper depend on the rotor speed and pressure drop with magnitudes decreasing as the rotor whirl frequency increases. The multiple-pocket gas damper seal provides substantially more damping than a conventional labyrinth seal of the same dimensions. The damper seal cross-coupled stiffness coefficients are small though sensitive to the inlet circumferential preswirl flow.

scholarly journals A Bulk-Flow Analysis of Multiple-Pocket Gas Damper Seals

1998 ◽  
Author(s):  
Jiming Li ◽  
Luis San Andrés ◽  
John Vance
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Current Model ◽  
Labyrinth Seal ◽  
Swirl Flow ◽  
Bulk Flow ◽  
Turbulent Shear ◽  
Dynamic Force ◽  
Gas Damper ◽  
Single Cavity

A bulk-flow model for calculation of the dynamic force characteristics in a single cavity, multiple-pocket gas damper seal is presented. Flow turbulence is accounted for by using turbulent shear stress parameters and Moody’s friction factors in the circumferential momentum equation. Zeroth order-equations describe the isothermal flow field for a centered seal, and first-order equations govern the perturbed flow for small amplitude rotor lateral motions. Comparisons to limited measurements from a four-pocket gas damper seal show the current model to predict well the mass flow rate and the direct damping coefficient. For a reference two-bladed teeth-on-stator labyrinth seal, the current model predicts similar rotordynamic coefficients when compared to results from a two control-volume bulk-flow model. Force coefficients from a reference single-cavity, four pocket gas damper depend on the rotor speed and pressure drop with magnitudes decreasing as the rotor whirl frequency increases. The multiple-pocket gas damper seal provides substantially more damping than a conventional labyrinth seal of the same dimensions. The damper seal cross-coupled stiffness coefficients are small though sensitive to the inlet circumferential pre-swirl flow.

A NONHOMOGENEOUS BULK FLOW MODEL FOR GAS IN LIQUID FLOW ANNULAR SEALS: AN EFFORT TO PRODUCE ENGINEERING RESULTS

2021 ◽  
pp. 1-31
Author(s):  
Xueliang Lu ◽  
Luis San Andres ◽  
Jing Yang
Keyword(s):  
Pressure Drop ◽  
Test Data ◽  
Liquid Flow ◽  
Flow Model ◽  
Bulk Flow ◽  
Experimental Results ◽  
Pure Liquid ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Direct Stiffness

Abstract Seals in multiple phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous BFM (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0 (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (~ 38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ~0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate) and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1.Compared to the test data, the two models generally under predict C and k by ~ 25%. Both models deliver a whirl frequency ratio (fw) ~ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ~0.35 as the GVF approaches 0.1. For the low pressure seal the flow is laminar, the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ~30 % below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal the fluid flow maintains the homogeneous character known at the inlet condition.

A Bulk-Flow Model of Angled Injection Lomakin Bearings

2002 ◽  
Author(s):  
Luis San Andre´s ◽  
Thomas Soulas ◽  
Florence Challier ◽  
Patrice Fayolle
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Performance ◽  
Bulk Flow ◽  
Computational Method ◽  
Design Parameters ◽  
Dynamic Force ◽  
Injection Angle ◽  
Flow Equations ◽  
Force Coefficients

The paper introduces a bulk-flow model for prediction of the static and dynamic force coefficients of angled injection Lomakin bearings. The analysis accounts for the flow interaction between the injection orifices, the supply circumferential groove, and the thin film lands. A one control-volume model in the groove is coupled to a bulk-flow model within the film lands of the bearing. Bernoulli-type relationships provide closure at the flow interfaces. Flow turbulence is accounted for with shear stress parameters and Moody’s friction factors. The flow equations are solved numerically using a robust computational method. Comparisons between predictions and experimental results for a tangential-against-rotation injection water Lomakin bearing show the novel model predicts well the leakage and direct stiffness and damping coefficients. Computed cross-coupled stiffness coefficients follow the experimental trends for increasing rotor speeds and supply pressures, but quantitative agreement remains poor. A parameter investigation evidences the effects of the groove and land geometries on the Lomakin bearing flowrate and force coefficients. The orifice injection angle does not influence the bearing static performance, although it largely affects its stability characteristics through the evolution of the cross-coupled stiffnesses. The predictions confirm the promising stabilizing effect of the tangential-against-rotation injection configuration. Two design parameters, comprising the feed orifices area and groove geometry, define the static and dynamic performance of Lomakin bearing. The analysis also shows that the film land clearance and length have a larger impact on the Lomakin bearing rotordynamic behavior than its groove depth and length.

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.

A Novel Bulk-Flow Model for Pocket Damper Seals

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Thomas Chirathadam
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Pressure ◽  
Bulk Flow ◽  
Order System ◽  
Shear Stresses ◽  
Flow Area ◽  
Rotordynamic Coefficients ◽  
Recirculating Flow ◽  
Numerical Predictions

Abstract In this paper, a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes (CVs) for each circumferential pocket of the seal. The continuity, circumferential momentum, and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modeled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee–Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth- and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive–negative inlet preswirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behavior of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and preswirl ratio.

A Novel Bulk-Flow Model for Pocket Damper Seals

2019 ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Thomas Chirathadam
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Pressure ◽  
Bulk Flow ◽  
Order System ◽  
Shear Stresses ◽  
Flow Area ◽  
Rotordynamic Coefficients ◽  
Recirculating Flow ◽  
Numerical Predictions

Abstract In this paper a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes for each circumferential pocket of the seal. The continuity, circumferential momentum and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modelled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee-Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive-negative inlet pre-swirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behaviour of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and pre-swirl ratio.

A Bulk-Flow Model of Angled Injection Lomakin Bearings

2002 ◽  
Vol 129 (1) ◽  
pp. 195-204
Author(s):  
Luis San Andrés ◽  
Thomas Soulas ◽  
Patrice Fayolle
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Performance ◽  
Bulk Flow ◽  
Computational Method ◽  
Design Parameters ◽  
Dynamic Force ◽  
Injection Angle ◽  
Flow Equations ◽  
Force Coefficients

This paper introduces a bulk-flow model for prediction of the static and dynamic force coefficients of angled injection Lomakin bearings. The analysis accounts for the flow interaction between the injection orifices, the supply circumferential groove, and the thin film lands. A one control-volume model in the groove is coupled to a bulk-flow model within the film lands of the bearing. Bernoulli-type relationships provide closure at the flow interfaces. Flow turbulence is accounted for with shear stress parameters and Moody’s friction factors. The flow equations are solved numerically using a robust computational method. Comparisons between predictions and experimental results for a tangential-against-rotation injection water Lomakin bearing show that novel model well predicts the leakage and direct stiffness and damping coefficients. Computed cross-coupled stiffness coefficients follow the experimental trends for increasing rotor speeds and supply pressures, but quantitative agreement remains poor. A parameter investigation shows evidence of the effects of the groove and land geometries on the Lomakin bearing flowrate and force coefficients. The orifice injection angle does not influence the bearing static performance, although it largely affects its stability characteristics through the evolution of the cross-coupled stiffnesses. The predictions confirm the promising stabilizing effect of the tangential-against-rotation injection configuration. Two design parameters, comprised of the feed orifices area and groove geometry, define the static and dynamic performance of Lomakin bearing. The analysis also shows that the film land clearance and length have a larger impact on the Lomakin bearing rotordynamic behavior than its groove depth and length.

A Bulk Flow Model for Off-Centered Honeycomb Gas Seals

2002 ◽  
Vol 129 (1) ◽  
pp. 185-194 ◽  
Author(s):  
Thomas Soulas ◽  
Luis San Andres
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Honeycomb Seal ◽  
Rotor Eccentricity ◽  
Honeycomb Seals ◽  
Gas Seals

A computational analysis for prediction of the static and dynamic forced performance of gas honeycomb seals at off-centered rotor conditions follows. The bulk-flow analysis, similar to the two-control volume flow model of Kleynhans and Childs (1997, “The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals,” ASME J. Eng. Gas Turbines Power, 119, pp. 949–957), is brought without loss of generality into a single-control volume model, thus simplifying the computational process. The formulation accommodates the honeycomb effective cell depth, and existing software for annular pressure seals and is easily upgraded for damper seal analysis. An analytical perturbation method for derivation of zeroth- and first-order flow fields renders the seal equilibrium response and frequency-dependent dynamic force impedances, respectively. Numerical predictions for a centered straight-bore honeycomb gas seal shows good agreement with experimentally identified impedances, hence validating the model and confirming the paramount influence of excitation frequency on the rotordynamic force coefficients of honeycomb seals. The effect of rotor eccentricity on the static and dynamic forced response of a smooth annular seal and a honeycomb seal is evaluated for characteristic pressure differentials and rotor speeds. Leakage for the two seal types increases slightly as the rotor eccentricity increases. Rotor off-centering has a pronounced nonlinear effect on the predicted (and experimentally verified) dynamic force coefficients for smooth seals. However, in honeycomb gas seals, even large rotor center excursions do not sensibly affect the effective local film thickness, maintaining the flow azimuthal symmetry. The current model and predictions thus increase confidence in honeycomb seal design, operating performance, and reliability in actual applications.

A Bulk Flow Model for Off-Centered Honeycomb Gas Seals

2002 ◽  
Author(s):  
Thomas Soulas ◽  
Luis San Andres
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Forced Response ◽  
Bulk Flow ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Honeycomb Seal ◽  
Rotor Eccentricity ◽  
Honeycomb Seals ◽  
Gas Seals

A computational analysis for prediction of the static and dynamic forced performance of gas honeycomb seals at off-centered rotor conditions follows. The bulk-flow analysis, similar to the two-control volume flow model of Kleynhans and Childs [1], is brought without loss of generality into a single-control volume model, thus simplifying the computational process. The formulation accommodates the honeycomb effective cell depth, and existing software for annular pressure seals is easily upgraded for damper seal analysis. An analytical perturbation method for derivation of zeroth- and first-order flow fields renders the seal equilibrium response and frequency-dependent dynamic force impedances, respectively. Numerical predictions for a centered straight-bore honeycomb gas seal show good agreement with experimentally identified impedances, hence validating the model and confirming the paramount influence of excitation frequency on the rotordynamic force coefficients of honeycomb seals. The effect of rotor eccentricity on the static and dynamic forced response of a smooth annular seal and a honeycomb seal is evaluated for characteristic pressure differentials and rotor speeds. Leakage for the two seal types increases slightly as the rotor eccentricity increases. Rotor off-centering does have a pronounced non-linear effect on the predicted (and experimentally verified) dynamic force coefficients for smooth seals. However, in honeycomb gas seals, even large rotor center excursions do not sensibly affect the effective local film thickness, maintaining the flow azimuthal symmetry. The current model and predictions thus increase confidence in honeycomb seal design, operating performance and reliability in actual applications.

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