Rotordynamic Stability Predictions for Centrifugal Compressors Using a Bulk-Flow Model to Predict Impeller Shroud Force and Moment Coefficients

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Manoj K. Gupta ◽  
Dara W. Childs
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Hole Injection ◽  
Pump Impeller ◽  
Stability Margins ◽  
Rotordynamic Coefficients ◽  
Model Predictions

An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal-compressor impeller’s shroud and its housing along the impeller’s front and back sides. This development is an extension of analyses performed first by Childs (1989, ASME J. Vib. Acoust., Stress, Reliab. Des., 111, pp. 216–225) for pump impellers. The bulk-flow model is used to predict reaction force and moment coefficients for the impeller shroud. A labyrinth seal code developed by Childs and Scharrer ( 1986, ASME Trans. J. Eng. Gas Turbines Power, 108, pp. 325–331) is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor stage and also provides a boundary condition for the shroud calculations. Comparisons between the measured shroud moment coefficients by Yoshida et al. (1996, Proceedings of the 6th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2, pp. 151–160) and model predictions show reasonable agreements for the clearance flow and reaction moments. For the conditions considered, low Mach number flow existed in the shroud clearance areas and compressible-flow and incompressible-flow models produced similar predictions. Childs’ model predictions for the direct damping and cross-coupled stiffness coefficients of a pump impeller produced reasonable agreement; hence the present model was validated to the extent possible. A rotor model consisting of an overhung impeller stage supported by a nominally cantilevered rotor was analyzed for stability using the present bulk-flow model and an API standard Wachel–von Nimitz formula model (1981, J. Petrol. Technol., pp. 2252–2260). The bulk-flow model predicted significantly higher onset speeds of instability. Given that some compressors have been predicted to be comfortably stable using API standard Wachel–von Nimitz formula but have been unstable on the test stand, these results suggest that unidentified destabilizing forces and or moments are present in compressors. Seal rub conditions that arise from surge events and increase the seal clearances are simulated, showing that enlarged clearances increase the preswirl at the seals, thus increasing these seal’s destabilizing forces and reducing stability margins. These results are consistent with field experience. Predictions concerning the back shroud indicate that shunt-hole injection mainly acts to enhance stability by changing the flow field of the division wall or balance piston seals, not by influencing the back-shroud’s forces or moments. Effective swirl brakes at these seals also serve this purpose.

Rotordynamic Stability Predictions for Centrifugal Compressors Using a Bulk-Flow Model to Predict Impeller Shroud Force and Moment Coefficients

2006 ◽  
Author(s):  
Manoj K. Gupta ◽  
Dara W. Childs
Keyword(s):  
Flow Model ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Hole Injection ◽  
Pump Impeller ◽  
Stability Margins ◽  
Flow Models ◽  
Rotordynamic Coefficients ◽  
Model Predictions

An analysis is developed for a compressible bulk-flow model of the leakage path between a centrifugal-compressor impeller’s shroud and its housing along the impeller’s front and back sides. This development is an extension of analyses performed first by Childs [15] for pump impellers. The bulk-flow model is used to predict reaction force and moment coefficients for the impeller shroud. A labyrinth seal code developed by Childs and Scharrer [21] is used to calculate the rotordynamic coefficients developed by the labyrinth seals in the compressor stage and also provides a boundary condition for the shroud calculations. Comparisons between the measured shroud moment coefficients by Yoshida et al. [18] and model predictions show reasonable agreements for the clearance flow and reaction moments. For the conditions considered, low Mach number flow existed in the shroud clearance areas and compressible-flow and incompressible-flow models produced similar predictions. Childs’ model predictions for the direct damping and cross-coupled stiffness coefficients of a pump impeller produced reasonable agreement; hence the present model was validated to the extent possible. A rotor model consisting of an overhung impeller stage supported by a nominally cantilevered rotor was analyzed for stability using the present bulk-flow model and an API standard Wachel-formula model [10]. The bulk-flow model predicted significantly higher onset speeds of instability. Given that some compressors have been predicted to be comfortably stable using API standard Wachel-formula but have been unstable on the test stand, these results suggest that unidentified destabilizing forces and or moments are present in compressors. Seal rub conditions that arise from surge events and increase the seal clearances are simulated, showing that enlarged clearances increase the preswirl at the seals, thus increasing these seal’s destabilizing forces and reducing stability margins. These results are consistent with field experience. Predictions concerning the back shroud indicate that shunt-hole injection mainly acts to enhance stability by changing the flow field of the division wall or balance piston seals, not by influencing the back-shroud’s forces or moments. Effective swirl brakes at these seals also serves this purpose.

On the Thermodynamic Process in the Bulk-Flow Model for the Estimation of the Dynamic Coefficients of Labyrinth Seals

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Filippo Cangioli ◽  
Paolo Pennacchi ◽  
Giuseppe Vannini ◽  
Lorenzo Ciuchicchi ◽  
Andrea Vania ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Energy Equation ◽  
Flow Model ◽  
Experimental Tests ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Labyrinth Seals ◽  
State Problem ◽  
Rotordynamic Coefficients ◽  
Steady State Problem

The impact of sealing equipment on the stability of turbomachineries is a crucial topic because the power generation market is continuously requiring high rotational speed and high performance, leading to the clearance reduction in the seals. The accurate characterization of the rotordynamic coefficients generated by the seals is pivotal to mitigate instability issues. In the paper, the authors propose an improvement of the state-of-the-art one-control volume (1CV) bulk-flow model (Childs and Scharrer, 1986, “An Iwatsubo-Based Solution for Labyrinth Seals: Comparison to Experimental Results,” ASME J. Eng. Gas Turbines Power, 108(2), pp. 325–331) by considering the energy equation in the steady-state problem. Thus, real gas properties can be evaluated in a more accurate way because the enthalpy variation, expected through the seal cavities, is evaluated in the model. The authors assume that the enthalpy is not a function of the clearance perturbation; therefore, the energy equation is considered only in the steady-state problem. The results of experimental tests of a 14 teeth-on-stator (TOS) labyrinth seal, performed in the high-pressure seal test rig owned by GE Oil&Gas, are presented in the paper. Positive and negative preswirl ratios are used in the experimental tests to investigate the effect of the preswirl on the rotordynamic coefficients. Overall, by considering the energy equation, a better numerical estimation of the rotordynamic coefficients for the tests with the negative preswirl ratio has been obtained (as it results from the comparison with the experiments). Finally, the numerical results are compared with a reference bulk-flow model proposed by Thorat and Childs (2010, “Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1,” ASME J. Eng. Gas Turbines Power, 132(11), p. 112504), highlighting the improvement obtained.

Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions

2018 ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Paolo Pennacchi ◽  
Lorenzo Ciuchicchi ◽  
Leonardo Nettis ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Labyrinth Seal ◽  
Accurate Estimation ◽  
Stability Assessment ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Working Principle ◽  
The Stability

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists in reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements. Eventually, the experimental data are compared to numerical results obtained with the new bulk-flow model (BFM) introduced in this paper.

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.

Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Paolo Pennacchi ◽  
Lorenzo Ciuchicchi ◽  
Leonardo Nettis ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Flow Model ◽  
Labyrinth Seal ◽  
Accurate Estimation ◽  
Stability Assessment ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Working Principle ◽  
The Stability

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam, and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability, and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists of reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements. Eventually, the experimental data are compared to the numerical results obtained with the new bulk-flow model (BFM) introduced in this paper.

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 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.

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.

A Novel Bulk-Flow Model for Pocket Damper Seals

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Filippo Cangioli ◽  
Giuseppe Vannini ◽  
Thomas Chirathadam
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Dynamic Pressure ◽  
Bulk Flow ◽  
Order System ◽  
Shear Stresses ◽  
Flow Area ◽  
Rotordynamic Coefficients ◽  
Recirculating Flow ◽  
Numerical Predictions

Abstract In this paper, a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes (CVs) for each circumferential pocket of the seal. The continuity, circumferential momentum, and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modeled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee–Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth- and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive–negative inlet preswirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behavior of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and preswirl ratio.

Application of a Novel Rotordynamic Identification Method for Annular Seals With Arbitrary Elliptical Orbits and Eccentricities

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Wanfu Zhang ◽  
Qianlei Gu ◽  
Jiangang Yang ◽  
Chun Li
Keyword(s):  
Fluid Velocity ◽  
Reaction Force ◽  
Grid Method ◽  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Eccentricity Ratio ◽  
Rotordynamic Coefficients ◽  
Identification Method ◽  
Gas Seals ◽  
Annular Seals

The identification method using infinitesimal theory is proposed to predict rotordynamic coefficients of annular gas seals. The transient solution combined with moving grid method was unitized to obtain the fluid reaction force at a specific position under different whirling frequencies. The infinitesimal method is then applied to obtain the rotordynamic coefficients, which agrees well with published experimental results for both labyrinth seals and eccentric smooth annular seals. Particularly, the stability parameter of the effective damping coefficient can be solved precisely. Results show that the whirling frequency has little influence on direct damping coefficient, effective damping coefficient, and cross-coupled stiffness coefficient for the labyrinth seal. And the effective damping coefficients decrease as the eccentricity ratio increases. A higher eccentricity ratio tends to destabilize the seal system, especially at a low whirling frequency. Results also show that the fluid velocity in the maximum clearance in the seal leakage path is less than that in the minimum clearance. The inertial effect dominates the flow field. Then it results in higher pressure appearing in maximum clearances. The pressure difference aggravates the eccentricity of rotor and results in static instabilities of the seal system.

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