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.

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.

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 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.

Leakage and Dynamic Force Coefficients for Two Labyrinth Gas Seals: Teeth-on-Stator and Interlocking Teeth Configurations. A Computational Fluid Dynamics Approach to Their Performance

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Tingcheng Wu ◽  
Luis San Andrés
Keyword(s):  
Gas Turbines ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Rotor Speed ◽  
Frequency Range ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Gas Seals

Labyrinth gas seals (LSs) 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 are 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 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 the 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 1.5 Ω. 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 demonstrates that 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, “Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbines Power, 134(4), pp. 04250301–04250312) and Vannini et al. (2014, “Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data,” ASME J. Eng. Gas Turbines Power, 136(2), pp. 022501–022509.)

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 Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

Measurements Versus Predictions for the Dynamic Impedance of Annular Gas Seals—Part II: Smooth and Honeycomb Geometries

2002 ◽  
Vol 124 (4) ◽  
pp. 963-970 ◽  
Author(s):  
M. P. Dawson ◽  
D. W. Childs
Keyword(s):  
Control Volume ◽  
Test Facility ◽  
Radial Clearance ◽  
Cell Width ◽  
Volume Model ◽  
Numerical Predictions ◽  
Dynamic Impedance ◽  
Honeycomb Seals ◽  
Gas Seals ◽  
Honeycomb Cell

Results are presented from tests conducted using an experimental test facility to measure the leakage and dynamic impedance of smooth and honeycomb straight-bore annular gas seals. The test seals had a 114.3 mm (4.500 in.) bore with a length-to-diameter ratio of 0.75 and a nominal radial clearance of 0.19 mm (0.0075 in.). The honeycomb cell depth for both seals was 3.10 mm (0.122 in.), and the cell width was 0.79 mm (0.031 in.). Dynamic impedance and leakage measurements are reported using air at three supply pressures out to 1.72 Mpa (250 psi), three speeds out to 20,200 rpm, and exit-to-inlet pressure ratios of 40% and 50%. Comparisons to the predictions from the two-control-volume model of Kleynhans and Childs [1] are of particular interest. This model predicts that honeycomb seals do not fit the conventional frequency independent model for smooth annular gas seals. The experimental results verify this new theory. Numerical predictions from a computer program incorporating the new two-control-volume model of Kleynhans and Childs [1] correlate well with both measured seal leakage and dynamic impedances for the honeycomb seals.

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