Combined Navier–Stokes and Bulk-Flow Analysis of Hybrid Bearings: Radial and Angled Injection

2004 ◽  
Vol 127 (3) ◽  
pp. 557-567 ◽  
Author(s):  
M. Hélène ◽  
M. Arghir ◽  
J. Frêne
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Pressure Field ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Favourable Effect ◽  
Alternative Analysis ◽  
Pressure Pattern ◽  
Numerical Predictions

The present work deals with the Navier–Stokes and bulk-flow analysis of hybrid bearings intended for use in aerospace applications. These bearings are expected to work at high rotational speeds and high feeding pressures. In such a case, the pressure in the shallow pockets of the bearing is no longer constant and is influenced by hydrostatic and hydrodynamic effects. It has been shown in the literature that the recess pressure pattern can have an important influence on the dynamic characteristics of the bearing. The present work investigates the pressure field in the recess of centered hybrid bearings with radial and angled injection by using a numerical Navier–Stokes analysis. The recess pressure pattern is then subsequently characterized by combining these results with some parametric descriptions. For calculating the dynamic characteristics of the bearing, the parametric pressure pattern is then injected into a bulk-flow model. The proposed model is an alternative analysis to the one advanced by San Andrés [ASME J. Tribole, 112, pp. 699–707; 119, 179–187] and in order to evaluate the validity of the bulk-flow code, the numerical predictions are compared with experimental data taken from the literature for radial and angled injection. The favourable effect of the counter-rotating angled injection is then explained by using the velocity field issued from the Navier–Stokes analysis and the pressure field given by the bulk-flow model.

Combined Navier-Stokes and Bulk-Flow Analysis of Hybrid Bearings: Radial and Angled Injection

2004 ◽  
Author(s):  
Mathieu Helene ◽  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Pressure Field ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Favorable Effect ◽  
Alternative Analysis ◽  
Pressure Pattern ◽  
Numerical Predictions

The present work deals with the Navier-Stokes and bulk-flow analysis of hybrid bearings intended for use in aerospace applications. These bearings are expected to work at high rotational speeds and high feeding pressures. In such a case, the pressure in the shallow pockets of the bearing is no longer constant and is influenced by hydrostatic and hydrodynamic effects. It has been shown in the literature that the recess pressure pattern can have an important influence on the dynamic characteristics of the bearing. The present work investigates the pressure field in the recess of centered hybrid bearings with radial and angled injection by using a numerical Navier Stokes analysis. The recess pressure pattern is then subsequently characterized by combining these results with some parametric descriptions. For calculating the dynamic characteristics of the bearing, the parametric pressure pattern is then injected into a bulk-flow model that is an alternative analysis of the one introduced by San Andre´s [3, 4]. In order to evaluate the validity of the bulk-flow code, the numerical predictions are compared with experimental data taken from the literature for radial and angled injection. The favorable effect of the counter-rotating angled injection is then explained by using the velocity field issued from the Navier Stokes analysis and the pressure field given by the bulk-flow model.

Analysis of Tangential-Against-Rotation Injection Lomakin Bearings

2003 ◽  
Author(s):  
Mihai Arghir ◽  
Mathieu He´le`ne ◽  
Jean Frene
Keyword(s):  
Thin Film ◽  
Dynamic Characteristics ◽  
Flow Model ◽  
Flow Equation ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Thin Film Model ◽  
High Reynolds ◽  
Annular Seals

This work presents a thin film flow model for analyzing the static and dynamic characteristics of centered, eccentric or misaligned tangential-against-rotation injection Lomakin bearings. The Lomakin bearing is a recent device intended for use in modern turbomachinery and having characteristics similar to hybrid bearings. It can be described as an ensemble of two opposing straight annular seals separated by a circumferential feeding groove. The fluid is supplied to the groove via orifice restrictors. Their tangential inclination generates an against-rotation circumferential flow in the groove that further penetrates into the thin film. This effect, known from annular seals as the pre-rotation speed, improves the dynamic characteristics of the bearing. The zero and first order analyses are carried out by recognizing the crucial importance of taking into account the interaction between the flow in the thin film lands, the circumferential groove and the supply orifices. Due to the high Reynolds number regime, the land flow is governed by the two dimensional thin film inertia equations (the “bulk flow” model). A one-dimensional circumferential flow dominated by inertia forces is assumed to take place in the groove and is described by an appropriate bulk flow equation. The flows in the supply orifices, the groove and the thin film lands are linked together by the same mass flow rate balance algorithm as used for hydrostatic and hybrid bearings analysis. The algorithm is extended to Lomakin bearings by considering the groove areas surrounding each orifice as a row of intercommunicating feeding pockets. This approach enables the analysis of centered, eccentric or misaligned Lomakin bearings. Comparisons with water-lubricated test results are used to validate the present model. For the zero eccentricity case a good agreement is obtained for the cross-coupled stiffness and for the whirl frequency ratio. A parametric study shows the variation of the bearing characteristics with increasing static eccentricity or misalignment. The limits of the developed thin film model are further estimated by comparing the static and zero eccentricity thin film results with a full Navier Stokes calculation.

A Bulk-Flow Analysis of Static and Dynamic Characteristics of Eccentric Circumferentially-Grooved Liquid Annular Seals

2004 ◽  
Vol 126 (2) ◽  
pp. 316-325 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Differential Equations ◽  
Dynamic Characteristics ◽  
Pressure Field ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Bulk Flow ◽  
Elliptic Type ◽  
Flow Equations ◽  
Numerical Predictions ◽  
Annular Seals

The bulk-flow equations used for inertia dominated thin-film flows is an attractive model for the analysis of circumferentially grooved annular seals because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming. By using three types of control volumes and some user-tuned constants, the bulk-flow model can be used for calculating the static and the dynamic characteristics. Until now, this has been carried out for centered seals where the flow is governed by ordinary differential equations but no solutions have yet been given for eccentric working conditions. In this latter case, the model is governed by partial differential equations of an elliptic type. The main problem is that for describing the groove effects, the pressure field must incorporate the concentrated drop or recovery effects that occur at the interface between the groove and the land zone. This means that the numerical procedure used for solving the elliptic equations should be able to handle a pressure field having discontinuous values and discontinuous first order derivatives. In the present work, the method used for integrating the system of bulk-flow equations is the SIMPLE algorithm. The algorithm is extended for handling pressure jumps by adding two pressure values on each side of the discontinuity. These values are then expressed in terms of cell centered pressures by imposing the mass conservation and the generalized Bernoulli equation at the discontinuity. This numerical solution is original and has never previously been presented in the finite volume related literature. Comparisons between the numerical predictions (leakage flow rate and rotordynamic coefficients) and experimental data taken from the literature Marquette and Childs (1997) are subsequently presented for an eccentric ten-groove annular seal.

Analysis of Leakage Flow and Dynamic Characteristics in Floating Ring Seals for High Pressure Turbopump

2006 ◽  
Author(s):  
Yong-Bok Lee ◽  
Chang-Ho Kim ◽  
Wenbo Duan ◽  
Fulei Chu
Keyword(s):  
Dynamic Characteristics ◽  
Flow Model ◽  
Stokes Equations ◽  
Descent Method ◽  
Bulk Flow ◽  
Steepest Descent Method ◽  
Leakage Flow ◽  
Transform Method ◽  
Flow Equations ◽  
Numerical Predictions

Because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming, the bulk-flow model was used for calculating the static and the dynamic characteristics of floating ring seals. The bulk-flow model is governed by three partial differential equations on eccentric working conditions with steepest descent method to find the seal’s equilibrium position efficiently. A finite difference scheme has been used to solve the nonlinear governing equations. Compared to Nelson and Nguyen’s Fast Fourier Transform Method, this scheme has better consistency. Perturbation analysis of the flow variables yields a set of zeroth and first-order equations. The SIMPLE algorithm is used to integrate the system of bulk-flow equations. Comparisons of the numerical predictions (lock-up eccentricity ratio, leakage flow rate and rotordynamic coefficients) with Ha’s results, which were formulated using the Fourier series, and experimental data are presented subsequently.

A bulk-flow analysis of static and dynamic characteristics of floating ring seals

2007 ◽  
Vol 40 (3) ◽  
pp. 470-478 ◽  
Author(s):  
Wenbo Duan ◽  
Fulei Chu ◽  
Chang-Ho Kim ◽  
Yong-Bok Lee
Keyword(s):  
Dynamic Characteristics ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Static And Dynamic Characteristics

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.

Test Results for the Static and Rotordynamic Characteristics of a Long (L/D = 0.75) Smooth Seal in Two-Phase (Mainly Gas) Conditions With a 62-Bar Inlet Pressure

2020 ◽  
Author(s):  
Dung L. Tran ◽  
Dara W. Childs ◽  
Hari Shrestha ◽  
Min Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Gas Turbines ◽  
Flow Model ◽  
Dynamic Stiffness ◽  
Bulk Flow ◽  
Liquid Volume ◽  
Test Results ◽  
Two Phase ◽  
Static And Dynamic Characteristics ◽  
San Andres

Abstract Recent multiphase-pump developments encountered several rotordynamic issues with smooth balance-piston seals, creating a need to better understand the performance of annular seals under multiphase-flow operation. This paper presents measurements of static and dynamic characteristics of a long smooth seal (L/D = 0.75, D = 114.686 mm, and Cr = 0.200 mm) operating under pure- and mainly air condition in which air is mixed with silicone oil (PSF-5cSt). Tests are performed at a supply pressure of 62.1 bars-a, three rotation speeds (5, 10, 15 krpm), three pressure ratios (PRs) (0.6, 0.5, 0.4), for a range of inlet liquid volume fraction (LVFi) from 0% to 8%. The results are then compared to: (1) the previous test reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” J. Eng. Gas Turbines Power, 139(12), p. 122504) with similar testing condition but a different seal geometry (L/D = 0.65, D = 89.306 mm, and Cr = 0.188 mm) and (2) the predictions from a bulk-flow model developed by San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503). Results show a significant increase of direct dynamic stiffness KΩ as LVFi increases, especially at low PR. Test results reported by Zhang et al. (2017) has an opposite tendency of KΩ as an impact of increasing LVFi. Concerning cross-coupled dynamic stiffness kΩ and cross-coupled damping c, the results from Zhang et al. (2017) and the present results agree to the effects of changing speed, PR, and LVFi under pure- and mainly air conditions. As LVFi increases, direct damping C increases while test results reported by Zhang et al. (2017) showed no significant increase. Except for the direct dynamic stiffness and the impact of changing LVFi on the cross-coupled dynamic stiffness, the bulk-flow model of San Andrés (2012) predicts decently the tendencies and magnitudes of the rotordynamic coefficients.

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.

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.

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