Sensitivity Analysis of the One-Control Volume Bulk-Flow Model for a 14 Teeth-on-Stator Straight-Through Labyrinth Seal

2017 ◽  
Author(s):  
Filippo Cangioli ◽  
Paolo Pennacchi ◽  
Giacomo Riboni ◽  
Giuseppe Vannini ◽  
Lorenzo Ciuchicchi ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Friction Factor ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
Bulk Flow ◽  
Mathematical Treatment ◽  
Dynamic Coefficients ◽  
The One

Since the 80s, academic research in the rotordynamics field has developed mathematical treatment for the prediction of the dynamic coefficients of sealing components. Dealing with the straight-through labyrinth seal, Iwatsubo [1], at a first stage, and Childs [2], later on, have developed the one-control volume bulk flow model. The model allows evaluating the surrounding fluid forces acting on the rotor, analyzing the fluid dynamics within the seal: the continuity, circumferential momentum and energy equations are solved for each cavity. To consider axial fluid dynamics, correlations, aiming to estimate the leakage and the pressure distribution, are required. Several correlations have been proposed in the literature for the estimation of the leakage, of the kinetic energy carry-over coefficient (KE), of the discharge coefficient and of the friction factor. After decades of research in the field of seal dynamics, the bulk-flow model has been confirmed as the most popular code in the industries, however, it is not clear which is the best set of correlations for the prediction of seal dynamic coefficients. This paper allows identifying the most accurate combination of correlations to be implemented in the bulk-flow model. The correlations are related to: the leakage formula, the flow coefficient, the KE and the friction factor. Investigating the results of several models (32 models), which consider different sets of correlations, in comparison to the experimental data (performed by General Electric Oil & Gas), it is possible to observe the dependence, of the model correlations, on the operating conditions. The experimental results, performed using a 14 teeth-on-stator labyrinth seal, investigate several operating conditions of pressure drop.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

Measured Comparison of Leakage and Rotordynamic Characteristics for a Slanted-Tooth and a Straight-Tooth Labyrinth Seal

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Naitik J. Mehta ◽  
Dara W. Childs
Keyword(s):  
Inclination Angle ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Radial Clearance ◽  
Rotordynamic Coefficients ◽  
Seal Design ◽  
Number Of Teeth

Measured results are presented to compare rotordynamic coefficients and leakage of a slanted-tooth labyrinth seal and a straight-tooth labyrinth seal. Both seals had identical pitch, depth, and number of teeth. The teeth inclination angle of the teeth on the slanted-tooth labyrinth was 65 deg from the normal axis. Experiments were carried out at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10.2, 15.35, and 20.2 krpm, and a radial clearance of 0.2 mm (8 mils). One zero and two positive inlet preswirl ratios were used. The results show only minute difference in the rotordynamic coefficients between the two seals. The slanted-tooth labyrinth seal consistently leaked approximately 10% less at all conditions. Predictions were made using a one control volume bulk-flow model (1CVM) which was developed for a straight-tooth labyrinth seal design. 1CVM under-predicted the rotordynamic coefficients and the leakage.

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.

A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu ◽  
Hideaki Maeda ◽  
Ono Tomoki
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Friction Factor ◽  
Flow Model ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified bulk-flow model to predict the rotordynamic force coefficients of shallow depth circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance dg/ Cr = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle (α), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α. This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code the friction factor model (f = nRem) is modified with the CFD extracted penetration angle (α) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with a measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves (L/D = 0.5, dg/Cr = 2.5) serves to further validate the predictions of the modified bulk-flow model. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients in particular.

scholarly journals Design and Analysis of CFD Experiments for the Development of Bulk-Flow Model for Staggered Labyrinth Seal

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Filippo Cangioli ◽  
Paolo Pennacchi ◽  
Leonardo Nettis ◽  
Lorenzo Ciuchicchi
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Flow Model ◽  
Control Volume ◽  
Computer Experiments ◽  
Bulk Flow ◽  
Labyrinth Seals ◽  
Dynamic Coefficients ◽  
Rotor Dynamic

Nowadays, bulk-flow models are the most time-efficient approaches to estimate the rotor dynamic coefficients of labyrinth seals. Dealing with the one-control volume bulk-flow model developed by Iwatsubo and improved by Childs, the “leakage correlation” allows the leakage mass-flow rate to be estimated, which directly affects the calculation of the rotor dynamic coefficients. This paper aims at filling the lack of the numerical modelling for staggered labyrinth seals: a one-control volume bulk-flow model has been developed and, furthermore, a new leakage correlation has been defined using CFD analysis. Design and analysis of computer experiments have been performed to investigate the leakage mass-flow rate, static pressure, circumferential velocity, and temperature distribution along the seal cavities. Four design factors have been chosen, which are the geometry, pressure drop, inlet preswirl, and rotor peripheral speed. Finally, dynamic forces, estimated by the bulk-flow model, are compared with experimental measurements available in the literature.

scholarly journals A Bulk-Flow Analysis of Multiple-Pocket Gas Damper Seals

1998 ◽  
Author(s):  
Jiming Li ◽  
Luis San Andrés ◽  
John Vance
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Current Model ◽  
Labyrinth Seal ◽  
Swirl Flow ◽  
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 pre-swirl flow.

Measured Comparison of Leakage and Rotordynamic Characteristics for a Slanted-Tooth and a Straight-Tooth Labyrinth Seal

2013 ◽  
Author(s):  
Naitik J. Mehta ◽  
Dara W. Childs
Keyword(s):  
Inclination Angle ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Radial Clearance ◽  
Rotordynamic Coefficients ◽  
Seal Design ◽  
Number Of Teeth

Measured results are presented to compare rotordynamic coefficients and leakage of a slanted-tooth labyrinth seal and a straight-tooth labyrinth seal. Both seals had identical pitch, depth, and number of teeth. The teeth inclination angle of the teeth on the slanted-tooth labyrinth was 65° from the normal axis. Experiments were carried out at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10.2, 15.35, and 20.2 krpm, and a radial clearance of 0.2 mm (8 mils). One zero and two positive inlet preswirl ratios were used. The results show only minute difference in the rotordynamic coefficients between the two seals. The slanted-tooth labyrinth seal consistently leaked approximately 10% less at all conditions. Predictions were made using a one control volume bulk-flow model (1CVM) which was developed for a straight-tooth labyrinth seal design. 1CVM under-predicted the rotordynamic coefficients and the leakage.

A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu ◽  
Hideaki Maeda ◽  
Ono Tomoki
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Friction Factor ◽  
Flow Analysis ◽  
Operating Conditions ◽  
Bulk Flow ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models (BFMs) predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified BFM to predict the rotordynamic force coefficients of shallow depth, circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance dg/Cr = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle (α), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α. This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code, the friction factor model (f = nRem) is modified with the CFD extracted penetration angle (α) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with the measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves (L/D = 0.5, dg/Cr = 2.5) serves to further validate the predictions of the modified BFM. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients, in particular.

A Numerical Investigation of the Effect of Inlet Preswirl Ratio on Rotordynamic Characteristics of Labyrinth Seal

2017 ◽  
Author(s):  
Tomohiko Tsukuda ◽  
Toshio Hirano ◽  
Cori Watson ◽  
Neal R. Morgan ◽  
Brian K. Weaver ◽  
...  
Keyword(s):  
Flow Model ◽  
Three Dimensional ◽  
Axial Direction ◽  
Labyrinth Seal ◽  
Flow Fields ◽  
Bulk Flow ◽  
The Other ◽  
Circumferential Velocity ◽  
Stiffness Coefficients ◽  
Inlet Swirl

Full three-dimensional CFD simulations are carried out using ANSYS CFX to obtain the detailed flow field and to estimate the rotordynamic coefficients of a labyrinth seal for various inlet swirl ratios. Flow fields in the labyrinth seal with the eccentricity of the rotor are observed in detail and the detailed mechanisms that increase the destabilizing forces at high inlet swirl ratios are discussed based on the fluid governing equations associated with the flow fields. By evaluating the contributions from each term of the governing equation to cross coupled force, it is found that circumferential velocity and circumferential distribution of axial mass flow rate play key roles in generating cross coupled forces. In the case that circumferential velocity is high and decreases along the axial direction, all contributions from each term are positive cross coupled force. On the other hand, in the case that circumferential velocity is low and increases along the axial direction, one contribution is positive but the other is negative. Therefore, cross coupled force can be negative in the local chamber depending on the balance even if circumferential velocity is positive. CFD predictions of cross coupled stiffness coefficients and direct damping coefficients show better agreement with experimental results than a bulk flow model does by considering the force on the rotor in the inlet region. Cross coupled stiffness coefficients derived from the force on the rotor in the seal section agree well with those of the bulk flow model.

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