Complete Modeling of Squeeze Film Dampers Using the Bulk Flow Model

2008 ◽  
Author(s):  
Je´roˆme Gehannin ◽  
Mihai Arghir ◽  
Olivier Bonneau
Keyword(s):  
Thin Film ◽  
Numerical Analysis ◽  
Piston Ring ◽  
Flow Model ◽  
Flow Equation ◽  
Bulk Flow ◽  
Squeeze Film ◽  
Time Step ◽  
Squeeze Film Dampers ◽  
Mass Sources

The present work presents a bulk flow based numerical analysis of squeeze film dampers (SFD) provided with circumferential grooves, feeding orifices and piston ring sealing devices. This means that the bulk flow model for inertia dominated flow regimes (high Re) was adapted for taking into account thin film discontinuities, mass sources located in the thin film zone (for modelling feeding orifices) or on the boundaries (piston ring seals with open slots). In the present work the rotor is whirling on a centered whirl and the bulk flow equation are solved by following a time step integration.

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 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.

Squeeze film dampers supporting high-speed rotors: Fluid inertia effects

2019 ◽  
Vol 234 (1) ◽  
pp. 18-32 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Thin Film ◽  
Pressure Distribution ◽  
Closed Form ◽  
Hydrodynamic Pressure ◽  
Fluid Film ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Thin Film Equations ◽  
Squeeze Film Dampers ◽  
Reaction Forces

This work represents closed-form analytical expressions for the operating parameters for short-length open-ended squeeze film dampers, including the lubricant velocity profiles, hydrodynamic pressure distribution, and lubricant reaction forces. The proposed closed-form expressions provide an accelerated calculation of the squeeze film damper parameters, specifically for rotordynamics applications. In order to determine the analytical solutions for the squeeze film damper parameters, the thin film equations for lubricant are introduced in the presence of the influence of lubricant inertia. Subsequently, two different analytical techniques, namely the momentum approximation method, and the perturbation method are applied to the thin film equations. Moreover, the solution for the lubricant flow equations are analytically determined to represent closed-form expressions for the hydrodynamic pressure distribution and the velocity component profiles in squeeze film dampers. Additionally, the expressions for the hydrodynamic pressure distribution are integrated over the journal surface, either numerically or analytically by using Booker’s integrals, to develop expressions for the fluid film reaction forces. Lastly, the developed squeeze film damper models are incorporated into simulation models in Matlab and Simulink®, and the results are compared against a well-established force coefficient model to verify the accuracy of the calculations. The results of the simulations verify the effect of the lubricant inertia components, namely the convective and temporal (i.e., unsteady) inertia components on the squeeze film damper dynamics, including hydrodynamic pressure distribution and fluid film reaction forces. Additionally, the simulation results suggest a close agreement between the proposed models and the results in the literature.

The Effect of Oil Supply and Sealing Arrangements on the Performance of Squeeze-Film Dampers: An Experimental Study

1996 ◽  
Vol 210 (4) ◽  
pp. 221-232 ◽  
Author(s):  
M C Levesley ◽  
R Holmes
Keyword(s):  
Experimental Study ◽  
Piston Ring ◽  
Squeeze Film ◽  
Damping Capacity ◽  
Squeeze Film Damper ◽  
Oil Supply ◽  
Squeeze Film Dampers

This paper compares the effects on the damping capacity of a squeeze-film damper of (a) changing the number of oil-feed holes to the central circumferential oil supply groove, (b) changing the sealing arrangement from end-seals to piston-ring seals, and (c) changing the position of the circumferential supply groove. The conclusions are that much improved damping performance is achieved by the piston-ring sealed arrangement. Unlike the end-sealed arrangement it is very little adversely influenced by a reduction in the number of oil-feed holes. The damping offered by either sealing arrangement is influenced only marginally by repositioning the supply groove.

Numerical Analysis of Flexible Rotor With Nonlinear Bearings and Squeeze Film Dampers

2014 ◽  
Author(s):  
Jianming Cao ◽  
Timothy Dimond ◽  
Paul Allaire
Keyword(s):  
Fluid Film ◽  
Squeeze Film ◽  
Steam Turbines ◽  
Flexible Rotor ◽  
Time Step ◽  
Closed Form Solutions ◽  
Wide Range ◽  
Squeeze Film Dampers ◽  
Nodal Displacements ◽  
Nonlinear Components

This paper presents dynamic behaviors of a flexible rotor supported on nonlinear bearings and nonlinear squeeze film dampers. The nonlinear bearing and damper forces, which depend on instantaneous nodal displacements and velocities, are calculated at each time step through closed form solutions of Reynolds equation. Such combinations of fluid film bearings and squeeze film dampers are often used in industrial machines such as compressors and steam turbines to increase system damping. No previous works have studied the nonlinear time transient analysis of a fluid film bearing and damper combination. To describe the coupled motion of shaft, bearing and squeeze film damper, a method of assembling both the linear rotor and the nonlinear components is developed. The numerical transient analyses are applied to a 3-disk rotor supported with nonlinear short plain journal bearings and nonlinear short squeeze film dampers. Squeeze film dampers, introduced to the system, increase dynamic stability of the system under a wide range of system rotational speeds, and decrease the bearing forces under severe unbalance forces. Different nonlinear rotor dynamic behavior, such as sub-harmonic, super-harmonic and torus orbits are shown in transient analyses. This type of analysis can be employed to study whether a centering spring is required in the damper or not.

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

2011 ◽  
Author(s):  
Luis San Andre´s ◽  
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 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); 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 later previously ignored or largely under predicted.

Analysis of Squeeze Film Dampers Operating With Bubbly Lubricants

1999 ◽  
Vol 122 (1) ◽  
pp. 205-210 ◽  
Author(s):  
Luoyi Tao ◽  
Sergio Diaz ◽  
Luis San Andre´s ◽  
K. R. Rajagopal
Keyword(s):  
Continuum Model ◽  
Flow Model ◽  
Bubbly Flow ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Test Rig ◽  
Actual Operating ◽  
Squeeze Film Dampers ◽  
Initial Procedure ◽  
Reliable Design

Rotor-bearing systems supported on squeeze film dampers (SFDs) show large amplitude vibratory motions when traversing critical speeds. At these operating conditions air is drawn into the damper thin film clearance generating a bubbly mixture with the lubricant and producing SFD forces not readily predictable with currently available analysis. A continuum model is proposed for describing the motion of a bubbly fluid in an open ended SFD operating with circular centered journal orbits. Computed predictions for peak-peak dynamic pressures and fluid film forces agree reasonably well with experimental measurements conducted on a SFD test rig operating with a controlled air in oil mixture. The bubbly flow model provides an initial procedure towards the reliable design of SFDs in actual operating conditions. [S0742-4787(00)02601-1]

Pressure Distribution in Squeeze Film Dampers with Oil Hole Feed

1994 ◽  
Vol 208 (2) ◽  
pp. 105-112 ◽  
Author(s):  
P Y P Chen ◽  
E J Hahn
Keyword(s):  
Solution Procedure ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Power Series Solution ◽  
Transient Solution ◽  
Tabular Data ◽  
Primary Interest ◽  
Time Step ◽  
Squeeze Film Dampers ◽  
Damping Capability

To improve the damping capability of squeeze film dampers, oil hole feed rather than circumferential groove feed is a practical proposition. However, circular orbit response can no longer be assumed, significantly complicating the design analysis. This paper details a feasible transient solution procedure for such dampers, with particular emphasis on the additional difficulties due to the introduction of oil holes. It is shown how a trigonometric power series solution may be utilized to evaluate the oil hole pressure contributions, enabling appropriate tabular data to be compiled. The solution procedure is shown to be applicable even in the presence of flow restrictors, albeit at the expense of introducing an iteration at each time step. Though not of primary interest, the procedure is also applicable to dynamically loaded journal bearings with oil hole feed.

Algebraic Solution of the Horton-Izzard Turbulent Overland Flow Model of the Rising Hydrograph

1977 ◽  
Vol 8 (4) ◽  
pp. 249-256 ◽  
Author(s):  
Mohammad Akram Gill
Keyword(s):  
Differential Equation ◽  
Turbulent Flow ◽  
Flow Model ◽  
Overland Flow ◽  
Flow Equation ◽  
Algebraic Solution ◽  
Mixed Flow ◽  
Overland Flow Model

In the differential equation of the overland turbulent flow which was first postulated by Horton, Eq.(6), the value of c equals 5/3. For this value of c, the flow equation could not be integrated algebraically. Horton solved the equation for c = 2 and believed that his solution was valid for mixed flow. The flow equation with c = 5/3 is solved algebraically herein. It is shown elsewhere (Gill 1976) that the flow equation can indeed be integrated for any rational value of c.

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