Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- \( a_{ri} , a_{si} \) :
-
Length of the rotor and stator of the i-th cavity
- \( A_{i} , A_{0i} \) :
-
Unsteady and steady cross-sectional area of the i-th cavity
- \( B \) :
-
Step height
- \( C_{eff} \) :
-
Effective damping of the seal
- \( c_{xx} , c_{yy} \) :
-
Direct damping of the seal in the x and y-directions
- \( c_{xy} , c_{yx} \) :
-
Cross-coupled damping of the seal in the x and y-directions
- \( C \) :
-
Average direct damping of the seal
- \( Dh_{i} , Dh_{0i} \) :
-
Unsteady and steady hydraulic diameter of the i-th cavity
- \( e \) :
-
Absolute roughness of the rotor and stator surface
- \( F_{x} \left( t \right), F_{y} \left( t \right) \) :
-
Lateral forces acting on the rotor
- \( h_{i} , h_{0i} \) :
-
Unsteady and steady enthalpy of the i-th cavity
- \( H_{i} \) :
-
Perturbed clearance of the i-th cavity
- \( k_{xx} , k_{yy} \) :
-
Direct stiffness of the seal in the x and y-directions
- \( k_{xy} , k_{yx} \) :
-
Cross-coupled stiffness of the seal in the x and y-directions
- \( k \) :
-
Average cross-coupled stiffness of the seal
- \( \dot{m}_{i} , \dot{m}_{0i} \) :
-
Unsteady and steady mass flow rate in the i-th cavity
- \( NJ \) :
-
Number of teeth
- \( P_{i} , P_{0i} \) :
-
Unsteady and steady pressure in the i-th cavity
- \( r_{0} \) :
-
Radius of the circular orbit of the rotor
- \( R \) :
-
Rotor radius
- \( R_{i} \) :
-
Rotor radius in the tooth location
- \( s_{i} \) :
-
Clearance of the i-th cavity
- t :
-
time
- \( V_{i} , V_{0i} \) :
-
Unsteady and steady tangential velocity in the i-th cavity
- \( W \) :
-
Tooth width at the tip of the i-th cavity
- \( x\left( t \right), y\left( t \right) \) :
-
Rotor displacement in the lateral directions
- \( \dot{x}\left( t \right), \dot{y}\left( t \right) \) :
-
Velocity of the rotor displacement in the lateral directions
- \( \varepsilon \) :
-
Perturbation parameter
- ϑ :
-
Angular coordinate
- µ :
-
Kinematic viscosity of the fluid
- \( \rho_{i} , \rho_{0i} \) :
-
Unsteady and steady density in the i-th cavity
- \( \varsigma_{i} \) :
-
Speed of sound of the fluid in the i-th cavity
- \( \tau_{si} , \tau_{s0i} \) :
-
Unsteady and steady stator shear stress in the i-th cavity
- \( \omega \) :
-
Whirling speed of the orbit of the rotor
- \( \varOmega \) :
-
Rotational speed of the rotor
- BC:
-
Boundary condition
- BFM:
-
Bulk-flow model
- CFD:
-
Computational fluid dynamics
- HPSTR:
-
High-pressure seal test-rig
References
Cangioli, F., Pennacchi, P., Vania, A., Chatterton, S., Dang, P.V.: Analysis of the dynamic behavior of two high-pressure turbines for the detection of possible rub symptoms. In: Proceedings of ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, South Korea (2016). https://doi.org/10.1115/gt2016-56627
Kirk, R.: Labyrinth seal analysis for centrifugal compressor design—theory and practice. In: Second IFToMM International Conference on Rotordynamics, Tokyo (1986)
Wagner, N.G.: Reliable rotor dynamic design of high-pressure compressors based on test rig data. J. Eng. Gas Turbines Power 123(4), 849–856 (2000)
Childs, D.W., Scharrer, J.K.: An Iwatsubo-based solution for labyrinth seals: comparison to experimental results. J. Eng. Gas Turbines Power 108, 325–331 (1986)
Dang, P., Chatterton, S., Pennacchi, P., Vania, A., Cangioli, F.: An experimental study of nonlinear oil-film forces in a tilting-pad journal bearing. In: ASME Conference, Boston, USA (2015)
Dang, P., Chatterton, S., Pennacchi, P., Vania, A., Cangioli, F.: Investigation of load direction on a five-pad tilting pad journal bearing with variable clearance. In: Proceedings of the 14th IFToMM World Congress, Taipei, Taiwan (2015)
Iwatsubo, T.: Evaluation of instability forces of labyrinth seals in turbines or compressors. In: NASA CP 2133, Proceedings of a Workshop at Texas A&M University, Rotordynamic Instability Problems in High Performance Turbomachinery, pp. 205–222 (1980)
Sreedharan, S., Vannini, G., Mistry, H.: CFD assessment of rotordynamic coefficients in labyrinth seals. In: ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Düsseldorf, Germany (2014)
Cangioli, F., Pennacchi, P., Vannini, G., Ciuchicchi, L.: Effect of energy equation in one control-volume bulk-flow model for the prediction of labyrinth seal dynamic coefficients. Mech. Syst. Signal Process. 98, 594–612 (2018)
Moore, J.J.: Three-dimensional CFD rotordynamic analysis of gas labyrinth seals. J. Vib. Acoust. 125(4), 427–433 (2003)
Vannini, G., Cioncolini, S., Calicchio, V., Tedone, F.: Development of a high pressure test rig for centrifugal compressors internal seals characterization. In: Proceedings of the Fortieth Turbomachinery Symposium, vol. %1 di %2 Houston, Texas, 12–15 September 2011
Vannini, G., Cioncolini, S., Del Vescovo, G., Rovini, M.: Labyrinth seal and pocket damper seal high pressure rotordynamic test data. J. Eng. Gas Turbines Power 136(2), 022501 (2014)
Cangioli, F., Pennacchi, P., Vannini, G., Ciuchicchi, L., Vania, A., Chatterton, S., Dang, P.V.: On the thermodynamic process in the bulk-flow model for the estimation of the dynamic coefficients of labyrinth seals. J. Eng. Gas Turbines Power (2017). https://doi.org/10.1115/1.4037919
Cangioli, F., Chatterton, S., Pennacchi, P., Nettis, L., Ciuchicchi, L.: Thermo-elasto bulk-flow model for labyrinth seals in steam turbines. Tribol. Int. 119, 359–371 (2018)
Cangioli, F., Pennacchi, P., Riboni, G., Vannini, G., Ciuchicchi, L., Vania, A., Chatterton, S.: Sensitivity analysis of the one-control volume bulk-flow model for a 14 teeth-on-stator straight-through labyrinth seal. In: Proceedings of ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, Charlotte, NC (2017). https://doi.org/10.1115/gt2017-63014
Lalanne, M., Ferraris, G.: Rotordynamics Predictions in Engineering. Wiley, Chichester (1998)
Cangioli, F., Pennacchi, P., Nettis, L., Ciuchicchi, L.: Design and analysis of CFD experiments for the development of bulk-flow model for staggered labyrinth seal. Int. J. Rotating Mach. 2018, 1–16 (2018). Article no. 9357249
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix A
Appendix A
The experimental measurements and numerical predictions of the direct stiffness and cross-coupled damping coefficients are reported here for both the experiments. Additionally, the effective stiffness coefficients is shown (Figs. 11, 12 and 13).
Comparison of predictions and measurements of direct stiffness and cross-coupled damping coefficients as a function of the whirling speed for the experiment A.
Comparison of predictions and measurements of direct stiffness and cross-coupled damping coefficients as a function of the whirling speed for the experiment B.
Comparison of predictions and measurements of the effective damping coefficient as a function of the whirling speed for the experiment A and B.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Cangioli, F. et al. (2019). Development and Validation of a Bulk-Flow Model for Staggered Labyrinth Seals. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM. IFToMM 2018. Mechanisms and Machine Science, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-99262-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-319-99262-4_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99261-7
Online ISBN: 978-3-319-99262-4
eBook Packages: EngineeringEngineering (R0)