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 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 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 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.

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.

A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Luis San Andrés ◽  
Adolfo Delgado
Keyword(s):  
Test Data ◽  
Flow Model ◽  
Hydrodynamic Instability ◽  
Added Mass ◽  
Operating Conditions ◽  
Bulk Flow ◽  
Squeeze Film ◽  
Accurate Estimation ◽  
Force Coefficients ◽  
Process Gas

Oil seals in centrifugal compressors reduce leakage of the process gas into the support bearings and ambient. Under certain operating conditions of speed and pressure, oil seals lock, becoming a source of hydrodynamic instability due to excessively large cross coupled stiffness coefficients. It is a common practice to machine circumferential grooves, breaking the seal land, to isolate shear flow induced film pressures in contiguous lands, and hence reducing the seal cross coupled stiffnesses. Published tests results for oil seal rings shows that an inner land groove, shallow or deep, does not actually reduce the cross-stiffnesses as much as conventional models predict. In addition, the tested grooved oil seals evidenced large added mass coefficients while predictive models, based on classical lubrication theory, neglect fluid inertia effects. This paper introduces a bulk-flow model for groove oil seals operating eccentrically and its solution via the finite element (FE) method. The analysis relies on an effective groove depth, different from the physical depth, which delimits the upper boundary for the squeeze film flow. Predictions of rotordynamic force coefficients are compared to published experimental force coefficients for a smooth land seal and a seal with a single inner groove with depth equaling 15 times the land clearance. The test data represent operation at 10 krpm and 70 bar supply pressure, and four journal eccentricity ratios (e/c= 0, 0.3, 0.5, 0.7). Predictions from the current model agree with the test data for operation at the lowest eccentricities (e/c= 0.3) with discrepancies increasing at larger journal eccentricities. The new flow model is a significant improvement towards the accurate estimation of grooved seal cross-coupled stiffnesses and added mass coefficients; the latter was previously ignored or largely under predicted.

Pump Grooved Seals: A Computational Fluid Dynamics Approach to Improve Bulk-Flow Model Predictions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Tingcheng Wu ◽  
Luis San Andrés
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Mechanical Energy ◽  
Bulk Flow ◽  
Dynamic Force ◽  
Centrifugal Pumps ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Groove Seal ◽  
Rectangular Groove

In multiple stage centrifugal pumps, balance pistons, often comprising a grooved annular seal, equilibrate the full pressure rise across the pump. Grooves in the stator break the evolution of fluid swirl and increase mechanical energy dissipation; hence, a grooved seal offers a lesser leakage and lower cross-coupled stiffness than a similar size uniform clearance seal. To date, bulk-flow modelbulk-flow models (BFMs) expediently predict leakage and rotor dynamic force coefficients of grooved seals; however, they lack accuracy for any other geometry besides rectangular. Note that scalloped and triangular (serrated) groove seals are not uncommon. In these cases, computational fluid dynamics (CFD) models seals of complex shape to produce leakage and force coefficients. Alas, CFD is not yet ready for routine engineer practice. Hence, an intermediate procedure presently takes an accurate two-dimensional (2D) CFD model of a smaller flow region, namely a single groove and adjacent land, to produce stator and rotor surface wall friction factors, expressed as functions of the Reynolds numbers, for integration into an existing BFM and ready prediction of seal leakage and force coefficients. The selected groove-land section is well within the seal length and far away from the effects of the inlet condition. The analysis takes three water lubricated seals with distinct groove shapes: rectangular, scalloped, and triangular. Each seal, with length/diameter L/D = 0.4, has 44 grooves of shallow depth dg ∼ clearance Cr and operates at a rotor speed equal to 5,588 rpm (78 m/s surface speed) and with a pressure drop of 14.9 MPa. The method validity is asserted when 2D (single groove-land) and three-dimensional (3D) (whole seal) predictions for pressure and velocity fields are compared against each other. The CFD predictions, 2D and 3D, show that the triangular groove seal has the largest leakage, 41% greater than the rectangular groove seal does, albeit producing the smallest cross-coupled stiffnesses and whirl frequency ratio (WFR). On the other hand, the triangular groove seal has the largest direct stiffness and damping coefficients. The scalloped groove seal shows similar rotordynamic force coefficients as the rectangular groove seal but leaks 13% more. For the three seal groove types, the modified BFM predicts leakage that is less than 6% away from that delivered by CFD, whereas the seal stiffnesses (both direct and cross-coupled) differ by 13%, the direct damping coefficients by 18%, and the added mass coefficients are within 30%. The procedure introduced extends the applicability of a BFM to predict the dynamic performance of grooved seals with distinctive shapes.

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