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.

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.

Experimental Analysis of Floating Ring Annular Seals and Comparisons With Theoretical Predictions

2015 ◽  
Author(s):  
Antoine Mariot ◽  
Mihai Arghir ◽  
Pierre Hélies ◽  
Jérôme Dehouve
Keyword(s):  
Theoretical Model ◽  
High Speed ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Maximum Pressure ◽  
Friction Forces ◽  
Carbon Ring ◽  
Annular Seal ◽  
Annular Seals

Floating ring annular seals represent one of the solutions for controlling leakage in high speed rotating machinery. They are generally made of a carbon ring mounted in a steel ring for preserving their integrity. Low leakage is ensured by the small clearance of the annular space between the carbon ring and the rotor. Under normal operating conditions, the ring must be able to “float” on the rotor in order to accommodate its vibration. Impacts between the carbon ring and the rotor may occur when the annular seal is locked up against the stator and the amplitude of rotor vibrations are larger than the radial clearance. This situation is prohibited because it rapidly leads to the destruction of the carbon ring. The present work presents experimental results obtained for floating ring annular seals of 38 mm, tandem mounted in a buffer seal arrangement. The rotation speed was comprised between 50 Hz and 350 Hz and maximum pressure drop was 7 bar. For these operating conditions the floating ring follows the rotor vibrations without any impacts. Comparisons were made with a theoretical model based on the equations of motion of the floating ring driven by mass inertia forces, hydrostatic forces in the (main) annular seal and by friction forces on its radial face (also named the “nose” of the seal). The friction coefficient on the nose of the floating ring was estimated from Greenwood and Williamson’s model for mixed lubrication. The present analysis validates the theoretical model used for predicting the dynamic response of the floating ring for a given rotor motion.

Experimental Analysis of Floating Ring Annular Seals and Comparisons With Theoretical Predictions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Antoine Mariot ◽  
Mihai Arghir ◽  
Pierre Hélies ◽  
Jérôme Dehouve
Keyword(s):  
Theoretical Model ◽  
High Speed ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Maximum Pressure ◽  
Friction Forces ◽  
Carbon Ring ◽  
Annular Seal ◽  
Annular Seals

Floating ring annular seals represent one of the solutions for controlling leakage in high-speed rotating machinery. They are generally made of a carbon ring mounted in a steel ring for preserving their integrity. Low leakage is ensured by the small clearance of the annular space between the carbon ring and the rotor. Under normal operating conditions, the ring must be able to “float” on the rotor in order to accommodate its vibration. Impacts between the carbon ring and the rotor may occur when the annular seal is locked up against the stator and the amplitude of rotor vibrations are larger than the radial clearance. This situation is prohibited because it rapidly leads to the destruction of the carbon ring. The present work presents experimental results obtained for floating ring annular seals of 38 mm, tandem mounted in a buffer seal arrangement. The rotation speed was comprised of between 50 Hz and 350 Hz, and maximum pressure drop was 7 bar. For these operating conditions, the floating ring follows the rotor vibrations without any impacts. Comparisons were made with a theoretical model based on the equations of motion of the floating ring driven by mass inertia forces, hydrostatic forces in the (main) annular seal, and by friction forces on its radial face (also named the “nose” of the seal). The friction coefficient on the nose of the floating ring was estimated from Greenwood and Williamson's model for mixed lubrication. The present analysis validates the theoretical model used for predicting the dynamic response of the floating ring for a given rotor motion.

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.

Research on hydrodynamic pressure field causing by ship moving in mixed flow

2017 ◽  
Vol 136 ◽  
pp. 314-321
Author(s):  
Hui Deng ◽  
Zhi-hong Zhang ◽  
Ju-bin Liu ◽  
Chong Wang
Keyword(s):  
Pressure Field ◽  
Hydrodynamic Pressure ◽  
Mixed Flow

Modelling and Analysis of a Grout Delivery Mechanism in the Remote Spray Lining of Shafts

1996 ◽  
Author(s):  
Liu Hongzhao ◽  
E. Appleton
Keyword(s):  
Relative Velocity ◽  
Viscous Friction ◽  
Emission Angle ◽  
Inertia Force ◽  
Viscous Damping ◽  
Friction Forces ◽  
Viscous Friction Force ◽  
Full Discussion ◽  
Delivery Mechanism ◽  
Driving Torque

Abstract A thorough analysis on the characteristics of a grout delivery mechanism in the lining of shafts has been accomplished. The dynamic equation of this spraying mechanism has been established and can describe the system’s performance properties under different conditions of viscous friction forces. The analysis introduces a combined viscous damping coefficient c* and a ratio λ between viscous friction force and inertia force. It is proved theoretically that the relative velocity of the grout is less than the implicate velocity and the emission angle α described in the paper is always larger than 45 °. Numerical simulations are performed by feeding various different parameters into the model. A full discussion of the effects of different variables is presented. Additionally, a formula for calculating the driving torque and power is developed. These studies provide an understanding of the properties of this mechanism and should prove useful in guiding its design and operation.

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.

A Comparison of Static and Rotordynamic Characteristics for Two Types of Liquid Annular Seals With Parallelly Grooved Stator/Rotor

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Leakage Flow ◽  
Frequency Range ◽  
Flow Rates ◽  
Pressure Drops ◽  
Force Coefficients ◽  
Operation Conditions ◽  
Annular Seal ◽  
Annular Seals

Abstract Liquid annular seals with parallelly grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor–stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers, and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient computational fluid dynamics-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number, and geometry. The present transient computational fluid dynamics-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, and 8.27 bar), three rotational speeds (2 krpm, 4 krpm, and 6 krpm) and three inlet preswirl ratios (0, 0.5, and 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y. For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C. The GS-SR seal produces purely positive Ceff throughout the whirling frequency range for all operation conditions, while Ceff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency fco with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

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