About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Mihai Arghir ◽  
Antoine Mariot
Keyword(s):  
Working Conditions ◽  
Rotation Speed ◽  
Theoretical Explanation ◽  
Exit Section ◽  
Static Stiffness ◽  
High Eccentricity ◽  
Flow Equations ◽  
Annular Seal ◽  
Asme Paper ◽  
Annular Seals

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201) had clearly no choked exit section. The present work advances a theoretical explanation of results reported by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.

About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

2014 ◽  
Author(s):  
Mihai Arghir ◽  
Antoine Mariot
Keyword(s):  
Working Conditions ◽  
Rotation Speed ◽  
Theoretical Explanation ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Equations ◽  
Annular Seal ◽  
Theoretical Results ◽  
Specific Working ◽  
Annular Seals

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented in [1] by Childs and Arthur. This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented in [1] had clearly no choked exit section. The present work advances a theoretical explanation of results reported in [1]. The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Freˆne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons with the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint this behaviour is explained by the modification of the Lomakin effect that changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

2006 ◽  
Vol 129 (4) ◽  
pp. 1028-1034 ◽  
Author(s):  
Mihai Arghir ◽  
Cyril Defaye ◽  
Jean Frêne
Keyword(s):  
Static Stability ◽  
Radial Force ◽  
Exit Section ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Friction Forces ◽  
Choked Flow ◽  
Annular Seal ◽  
Quantitative Results ◽  
Gas Seals

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal, choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons to the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section, the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section, the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint, this behavior is explained by the modification of the Lomakin effect, which changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

scholarly journals Fluid Flow Equations for Rotordynamic Flows in Seals and Leakage Paths

2001 ◽  
Vol 124 (1) ◽  
pp. 176-181 ◽  
Author(s):  
Y. Hsu ◽  
C. E. Brennen
Keyword(s):  
Fluid Flow ◽  
Numerical Method ◽  
Bulk Flow ◽  
Experimental Measurements ◽  
Flow Equations ◽  
Flow Models ◽  
Annular Seal ◽  
Rotordynamic Forces ◽  
Annular Seals

Fluid-induced rotordynamic forces produced by the fluid in an annular seal or in the leakage passage surrounding the shroud of a pump or turbine, are known to contribute substantially to the potential excitation forces acting on the rotor. The present research explores some of the important features of the equations governing bulk-flow models of these flows. This in turn suggests methods which might be used to solve these bulk-flow equations in circumstances where the linearized solutions may not be accurate. This paper presents a numerical method for these equations and discusses comparison of the computed results with experimental measurements for annular seals and pump leakage paths.

Analytic Modeling of Floating Ring Annular Seals

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Mihai Arghir ◽  
Manh-Hung Nguyen ◽  
David Tonon ◽  
Jérôme Dehouve
Keyword(s):  
Working Conditions ◽  
Pressure Field ◽  
Hydrodynamic Pressure ◽  
Radial Clearance ◽  
Inertia Force ◽  
Friction Forces ◽  
Leakage Flow Rate ◽  
Annular Seal ◽  
Inertia Forces ◽  
Annular Seals

In order to avoid contact between the vibrating rotor and the stator, annular seals are designed with a relatively large radial clearance (∼100 μm) and, therefore, have an important leakage. The floating ring annular seal is able to reduce the leakage flow rate by using a much lower clearance. The seal is designed as a ring floating on the rotor in order to accommodate its vibrations. The pressure difference between the upstream and the downstream chambers is pressing the nose of the floating ring (secondary seal) against the stator. The forces acting on the floating ring are the resultant of the hydrodynamic pressure field inside the primary seal, the friction forces in the secondary seal, and the inertia forces resulting from the non-negligible mass of the ring. For proper working conditions, the ring of the annular seal must be able to follow the vibration of the rotor without any damage. Under the effect of the unsteady hydrodynamic pressure field (engendered by the vibration of the rotor), of the friction force, and of the inertia force, the ring will describe a periodic, a quasi-periodic, or a chaotic motion. Damage can come from heating due to friction in the secondary seal or from repeated impacts between the rotor and the ring. The present work presents an analytic model able to take into account only the synchronous periodic whirl motion of the floating ring.

Analytic Modelling of Floating Ring Annular Seals

2011 ◽  
Author(s):  
Mihai Arghir ◽  
Manh-Hung Nguyen ◽  
David Tonon ◽  
Je´roˆme Dehouve
Keyword(s):  
Working Conditions ◽  
Pressure Field ◽  
Hydrodynamic Pressure ◽  
Radial Clearance ◽  
Inertia Force ◽  
Friction Forces ◽  
Leakage Flow Rate ◽  
Annular Seal ◽  
Inertia Forces ◽  
Annular Seals

In order to avoid contact between the vibrating rotor and the stator annular seals are designed with a relatively large radial clearance (∼100 μm) and therefore have an important leakage. The floating ring annular seal is able to reduce the leakage flow rate by using a much lower clearance. The seal is designed as a ring floating on the rotor in order to accommodate its vibrations. The pressure difference between the upstream and the downstream chambers is pressing the nose of the floating ring (secondary seal) against the stator. The forces acting on the floating ring are the resultant of the hydrodynamic pressure field inside the primary seal, the friction forces in the secondary seal and the inertia forces resulting from non-negligible mass of the ring. For proper working conditions the ring of the annular seal must be able to follow the vibration of the rotor without any damage. Under the effect of the unsteady hydrodynamic pressure field (engendered by the vibration of the rotor), of the friction force and of the inertia force, the ring will describe a periodic, a quasi-periodic or a chaotic motion. Damage can come from heating due to friction in the secondary seal or from repeated impacts between the rotor and the ring. The present work presents an analytic model able to take into account only the synchronous periodic whirl motion of the floating ring.

The Numerical Analysis of the Velocity and Pressure Distribution of the Oil Film in Heavy Hydrostatic Thrust Bearing

2014 ◽  
Vol 541-542 ◽  
pp. 658-662
Author(s):  
Jian Li ◽  
Yuan Chen ◽  
Yang Chun Yu ◽  
Zhu Xin Tian ◽  
Yu Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Pressure Distribution ◽  
Working Conditions ◽  
Thrust Bearing ◽  
Rotation Speed ◽  
The Other ◽  
Surface Load ◽  
Oil Film ◽  
Volume Method

To study the velocity and pressure distribution of the oil film in a heavy hydrostatic thrust bearing, a mathematical model of the velocity is proposed and the finite volume method (FVM) has been used to simulate the flow field under different working conditions. Some pressure experiments were carried out and the results verified the correctness of the simulation. It is concluded that the pressure distribution varies small under different rotation speed when the surface load on the workbench is constant. But the velocity of the oil film is influenced greatly by the rotation speed. When the rotation speed of the workbench is as quick as enough, the velocity of the oil film on one radial side of the pad will be zero, that is to say the lubrication oil will be drained from the other three sides of the recess.

Numerical Investigation on the Leakage and Static Stability Characteristics of Pocket Damper Seals at High Eccentricity Ratios

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Static Stability ◽  
Operating Conditions ◽  
Eccentricity Ratio ◽  
Static Stiffness ◽  
Flow Conditions ◽  
Experiment Data ◽  
High Eccentricity ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Gas Seals

Annular gas seals for compressors and turbines are designed to operate in a nominally centered position in which the rotor and stator are at concentric condition, but due to the rotor–stator misalignment or flexible rotor deflection, many seals usually are suffering from high eccentricity. The centering force (represented by static stiffness) of an annular gas seal at eccentricity plays a pronounced effect on the rotordynamic and static stability behavior of rotating machines. The paper deals with the leakage and static stability behavior of a fully partitioned pocket damper seal (FPDS) at high eccentricity ratios. The present work introduces a novel mesh generation method for the full 360 deg mesh of annular gas seals with eccentric rotor, based on the mesh deformation technique. The leakage flow rates, static fluid-induced response forces, and static stiffness coefficients were solved for the FPDS at high eccentricity ratios, using the steady Reynolds-averaged Navier–Stokes solution approach. The calculations were performed at typical operating conditions including seven rotor eccentricity ratios up to 0.9 for four rotational speeds (0 rpm, 7000 rpm, 11,000 rpm, and 15,000 rpm) including the nonrotating condition, three pressure ratios (0.17, 0.35, and 0.50) including the choked exit flow condition, two inlet preswirl velocities (0 m/s, 60 m/s). The numerical method was validated by comparisons to the experiment data of static stiffness coefficients at choked exit flow conditions. The static direct and cross-coupling stiffness coefficients are in reasonable agreement with the experiment data. An interesting observation stemming from these numerical results is that the FPDS has a positive direct stiffness as long as it operates at subsonic exit flow conditions; no matter the eccentricity ratio and rotational speed are high or low. For the choked exit condition, the FPDS shows negative direct stiffness at low eccentricity ratio and then crosses over to positive value at the crossover eccentricity ratio (0.5–0.7) following a trend indicative of a parabola. Therefore, the negative static direct stiffness is limited to the specific operating conditions: choked exit flow condition and low eccentricity ratio less than the crossover eccentricity ratio, where the pocket damper seal (PDS) would be statically unstable.

scholarly journals Transient CFD Simulation on Dynamic Characteristics of Annular Seal under Large Eccentricities and Disturbances

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4056
Author(s):  
Kai Zhang ◽  
Xinkuo Jiang ◽  
Shiyang Li ◽  
Bin Huang ◽  
Shuai Yang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Cfd Simulation ◽  
Resonance Region ◽  
Nonlinear Dynamic Model ◽  
Annular Seal ◽  
Transient Simulations ◽  
Computational Fluid Dynamics Cfd ◽  
Annular Seals

Annular seals of turbomachinery usually suffer from various degrees of eccentricities and disturbances due to the rotor–stator misalignment and radial loads, while the discussion of annular seal under both large static eccentricities and dynamic disturbances is relatively limited. In this paper, the applicability of linear assumption and reliability of nonlinear dynamic model for eccentric annular seals under large eccentricities and disturbances is discussed based on the investigation of seals with various rotor motions through computational fluid dynamics (CFD). After the validation of transient CFD methods by comparison with experimental and bulk theory results, the dynamic behaviors of annular seal are analyzed by adopting both direct transient simulations and the nonlinear Muszynska model. The results show that the nonlinear dynamic model based on rotor circular whirls around seal center can predict the fluid excitations of different types of rotor motions well under small static eccentricities, while it is limited severely with large static eccentricities, which indicates that the dynamic characteristics of annular seal under large eccentricities are related with the rotor’s motion ways. The paper provides a reference for studies of rotor–seal system with complex rotor motions considering radial loads or running across the resonance region.

Numerical Modeling of Static and Rotordynamic Characteristics for Three Types of Helically Grooved Liquid Annular Seals

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Perturbation Method ◽  
Navier Stokes ◽  
Force Coefficients ◽  
Numerical Predictions ◽  
Curve Fit ◽  
Annular Seal ◽  
Frequency Independent ◽  
Computational Fluid Dynamics Cfd ◽  
Multiple Reference ◽  
Annular Seals

Abstract This paper deals with numerical predictions of the leakage flowrates, drag power, and rotordynamic force coefficients for three types of helically grooved liquid annular seals, which include a liquid annular seal with helically grooved stator (GS/SR seal), one with helically grooved rotor (SS/GR seal), and one with helical grooves on stator and rotor (GS/GR seal). A novel transient computational fluid dynamics (CFD)-based perturbation method was proposed for the predictions of the leakage flowrates, drag power, and rotordynamic force coefficients of helically grooved liquid annular seals. This method is based on the unsteady Reynolds-averaged Navier–Stokes (RANS) solution with the mesh-deformation technique and the multiple reference frame theory. The time-varying fluid-induced forces acting on the rotor/stator surface were obtained as a response to the time-dependent perturbation of the seal stator surface with the periodic motion, based on the multiple-frequency elliptical-orbit stator whirling model. The frequency-independent rotordynamic force coefficients were determined using curve fit and fast Fourier transform (FFT) in the frequency domain. The CFD-based method was adequately validated by comparisons with the published experiment data of leakage flowrates and fluid response forces for three types of helically grooved liquid annular seals. Based on the transient CFD-based perturbation method, numerical results of the leakage flowrates, drag powers, and rotordynamic force coefficients were presented and compared for three types of helically grooved liquid annular seals at five rotational speeds (n = 0.5 krpm, 1.0 krpm, 2.0 krpm, 3.0 krpm, and 4.0 krpm), paying special attention to the effective stiffness coefficient and effective damping coefficient.

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