scholarly journals An Approach to Calculate Leakage Flow, Stiffness and Damping of Annular Seals in Turbulent Flow Using Lubrication Theory, Part II: Results

2007 ◽  
Vol 2 (4) ◽  
pp. 99-104
Author(s):  
Satyam Shivam Gautam ◽  
Mihir Kumar Ghosh
Keyword(s):  
Turbulent Flow ◽  
Lubrication Theory ◽  
Leakage Flow ◽  
Stiffness And Damping ◽  
Annular Seals

scholarly journals Dynamic analysis of liquid annular seals with herringbone grooves on the rotor based on the perturbation method

2018 ◽  
Vol 5 (6) ◽  
pp. 180101 ◽  
Author(s):  
Lulu Zhai ◽  
Zhang Zhenjie ◽  
Chi Zhonghuang ◽  
Guo Jia
Keyword(s):  
Dynamic Characteristics ◽  
Operating Conditions ◽  
Geometric Parameters ◽  
Leakage Flow ◽  
Flow Rates ◽  
Rotordynamic Coefficients ◽  
Sealing Performance ◽  
Spiral Angle ◽  
Herringbone Grooves ◽  
Annular Seals

Annular seals have significant effects on the hydraulic and rotordynamic performances of turbomachinery. In this paper, an analysis method for calculating the leakage flow rates and dynamic characteristics of liquid annular seals with herringbone grooves on the rotor is proposed and verified. Leakage flow rates and dynamic characteristics of the model seals under different operating conditions are theoretically analysed and compared with those of plain and spiral-grooved seals of the same size. In addition, the influence of geometric parameters such as spiral angle and the lengths of the constituent parts on the sealing and rotordynamic coefficients of seals with herringbone grooves are also discussed. The results show that seals with herringbone grooves have better sealing performance, while providing better support actions and damping characteristics than the other two seal types under the same operating conditions. The seal geometric parameters including spiral angle, the lengths of the constituent parts and the clearance value have a significant influence on the dynamic characteristics of seals with herringbone grooves.

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.

Numerical Comparison of Static and Rotordynamic Characteristics for a Grooved-Stator/Smooth-Rotor and a Smooth-Stator/Grooved-Rotor Liquid Annular Seals

2019 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Working Fluid ◽  
Leakage Flow ◽  
Frequency Range ◽  
Flow Rates ◽  
Pressure Drops ◽  
Force Coefficients ◽  
Operation Conditions ◽  
Annular Seal ◽  
Positive Direct ◽  
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 CFD-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 CFD-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, 8.27 bar), three rotational speeds (2 krpm, 4 krpm, 6 krpm) and three inlet preswirl ratios (0, 0.5, 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.

The Effects of Geometry and Inertia on Face Seal Performance—Turbulent Flow

1968 ◽  
Vol 90 (2) ◽  
pp. 342-350 ◽  
Author(s):  
H. J. Sneck
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Power Law ◽  
Apparent Viscosity ◽  
Lubrication Theory ◽  
Inertial Effects ◽  
Face Seal ◽  
Geometric Deviations ◽  
The Ideal

The “short bearing” equation of lubrication theory, modified to include the inertial effects, is used to study the influence of geometric deviations from the ideal. The turbulent nature of the flow is described by an isotropic apparent viscosity and a power-law velocity distribution. It is found that geometric deviations from the ideal are less influential than in laminar flow.

scholarly journals Numerical Analyses of Static Characteristics of Liquid Annular Seals Based on 2D LBM-LES Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhenjie Zhang ◽  
Lulu Zhai ◽  
Jia Guo ◽  
Zuchao Zhu ◽  
Guoyou Chen
Keyword(s):  
Theoretical Method ◽  
Velocity Model ◽  
Empirical Method ◽  
Operating Conditions ◽  
Maximum Deviation ◽  
Leakage Flow ◽  
Static Characteristics ◽  
Flow Rates ◽  
Calculating Model ◽  
Annular Seals

Static characteristics and leakage flow rates of liquid annular seals have great influences on the hydraulic efficiency of turbomachinery. In this paper, a two-dimensional (2D) mathematical model for predicting the leakage flow rates and static characteristics of liquid seal is established, based on the lattice Boltzmann method (LBM) combined with the D2G9 velocity model for incompressible fluid and large eddy simulation (LES) turbulence model, in which the transformation equation of reference pressure is developed with the Bernoulli equation. Moreover, the proposed model is validated by comparing with the experimental results, calculation results based on the finite volume method (FVM), and the results based on the empirical method of three seals under different operating conditions. The comparisons show that the maximum deviation in leakage prediction of the calculating model based on 2D LBM is 4%, and this calculating model will effectively improve the leakage prediction accuracy of the seals compared with the FVM and theoretical method.

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

2019 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Perturbation Method ◽  
Leakage Flow ◽  
Centrifugal Pumps ◽  
Flow Rates ◽  
Force Coefficients ◽  
Numerical Predictions ◽  
Multi Stage ◽  
Annular Seal ◽  
Helical Grooves ◽  
Annular Seals

Abstract This paper deals with numerical predictions of the leakage flow rates, 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). These seals are frequently used for multiple-stage centrifugal pumps as they have the advantage of low leakage (even to zero) due to the “pumping effect” of the helical grooves. However, the static and rotordynamic characteristics of helically-grooved liquid annular seals still are not fully understood, and even more pronounced is the lack of effective numerical models in the literature. A novel transient CFD-based perturbation method was proposed for the predictions of the leakage flow rates, 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 to the published experiment data of leakage flow rates 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 flow rates, 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. Results show that the GS/GR seal has the best sealing capability, followed by the GS/SR seal and then the SS/GR seal. The leakage flow rate of all three helically-grooved seals monotonically decreases with the increasing rotational speed. The GS/SR seal possesses the best stiffness and damping capability, followed by the SS/GR seal and then the GS/GR seal. Rotordynamic instability problems are more likely caused by the GS/GR seal in multi-stage centrifugal pumps. From a rotordynamic viewpoint, the GS/SR helically-grooved liquid annular seal is a better seal concept for multi-stage centrifugal pumps.

An Expression of Reynolds Stresses in Turbulent Lubrication Theory

1992 ◽  
Vol 114 (1) ◽  
pp. 57-60 ◽  
Author(s):  
A. K. Tieu ◽  
P. B. Kosasih
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Flow ◽  
Low Reynolds Number ◽  
Stress Gradient ◽  
Lubrication Theory ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Shear Stress Gradient ◽  
Low Reynolds

This paper proposes an alternative model of Reynolds stresses for turbulent lubrication theory. The approach relies on Prandtl’s mixing length theory which is based on a modified Van Driest mixing formula [1]. However, unlike the previous theories [2, 3] the proposed equation is capable of accounting for the effect of shear stress gradient on the mixing length. Thus it is well suited to turbulent flow analysis in bearings where the presence of shear stress gradient due to the effect of pressure gradient should be considered. A series of velocity measurements in thin channels in the low Reynolds number turbulent flow range are analysed using the theory. The data analysis shows a strong effect of shear stress gradient on the viscous sublayer in the low Reynolds number regime. As a result, a new model of mixing length applicable to the turbulent lubrication analysis in thin film at low or high Reynolds numbers or under low or high shear stress gradient is presented.

Measurement of Static and Dynamic Properties of a Tilting Pad Bearing and Comparison With Theory

1993 ◽  
Author(s):  
Thomas Bonner ◽  
John H. Vohr
Keyword(s):  
Dynamic Properties ◽  
Lubrication Theory ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Phase Angles ◽  
Good Agreement

Abstract Measurements were made of the static and dynamic properties of a seven inch diameter, four-pad, tilting pad bearing with both centrally pivoted and 60% offset pads. Data was recorded at 1500, 1800 and 3000 RPM and covered a range of Sommerfeld numbers from .055 to .625. Dynamic properties were measured by applying unbalance weights of various magnitudes to the rotor and measuring the synchronous response amplitudes and phase angles. Good agreement was obtained between measured properties and those predicted using linearized stiffness and damping coefficients obtained from isoviscous lubrication theory.

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