Study on Leakage Performance and Rotordynamic Characteristics of a Novel Semi-Y Type Labyrinth Seal
Abstract
:1. Introduction
2. The Model of SYLS Structure
3. Computational Method
3.1. Structural Dimension
3.2. Solution Settings
3.3. Validation of the Computational Model
3.4. Mesh Independence Verification
4. Result and Discussion
4.1. Static Characteristics
4.1.1. Effects of Pressure Drop and Tilt Angle on Leakage
4.1.2. Effects of Clearance on Leakage
4.1.3. Effects of the Height of Rotor Teeth on Leakage
4.2. Dynamic Characteristics
4.2.1. Influence of Tilt Angle on Dynamic Coefficients for Different Pressure Drops and Rotation Speeds
4.2.2. Influence of Clearance on Dynamic Coefficients for Different Pressure Drops or Rotation Speeds
4.2.3. Whirl Frequency Ratio
5. Conclusions
- (1)
- The numerical results calculated by the standard k-ε turbulent model present a good agreement with the experimental results. The maximum error and minimum errors are 2.81% and 1.87%, respectively.
- (2)
- The leakage increases with the increase in pressure drop and clearance. However, the leakage presents the trend of secondary curves, and it reaches the peak value at θ = 70°; in other words, the leakage performance is the worst for the SYLS structure at θ = 70°. In addition, the leakage gets the trough value at θ = 135°, which is about 30% lower than ILS.
- (3)
- The direct stiffness K of the SYLS structure at θ = 45° shows a sharp decline with the increase in pressure drop, while it reveals a slight sensitivity at θ = 135°. The reason is that the throttling function generated by the tip of rotor teeth causes a great pressure drop between the upper side and lower side of the rotor teeth, which changes the radial force. The dynamic coefficients for different clearances increase with the increase in pressure drop except for the direct stiffness K. Moreover, the cross-coupled stiffness k and the direct damping C are the largest at Cr = 0.1 mm.
- (4)
- The low-pressure drop and high rotation speed can induce a small whirl frequency ratio, which is helpful for the stability of the SYLS structure. The SYLS structure presents the best stability performance at θ = 45°. In addition, the whirl frequency ratio is sensitive to pressure drop and exceeds one under the conditions of Cr = 0.1 mm and ω = 1000 rpm.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Hs | Stator tooth height (mm) |
Hr | Rotor tooth height (mm) |
Hv | Vertical height of rotor tooth (mm) |
Cr | Tip clearance (mm) |
D | Rotor diameter (mm) |
L | Seal length (mm) |
Lp | Pitch between rotor teeth and static teeth (mm) |
Bs | Stator tooth width (mm) |
Br | Rotor tooth width (mm) |
Bc | Cavity width (mm) |
Tilt angle (°) | |
Z | Tooth number |
Q | Leakage (kg/s) |
Δp | Pressure drop (MPa) |
Whirling speed (rpm) | |
Rotating speed (rpm) | |
Fx, Fy | Seal reaction force in x and y axis (N) |
Fr, Ft | Seal reaction force in radial and tangential direction (N) |
Kxx, Kyy | Direct stiffness coefficient in x and y direction (N/m) |
Kxy, Kyx | Cross-coupled stiffness coefficient in x and direction (N/m) |
Cxx, Cyy | Direct damping coefficient in x and y direction (N·s/m) |
Cxy, Cyx | Cross-coupled damping coefficient in x and y direction (N·s/m) |
Mxx, Myy | Direct added mass in x and y direction (kg) |
Mxy, Myx | Cross-coupled added mass in x and y direction (kg) |
K | Direct stiffness coefficient (N/m) |
k | Cross-coupled stiffness coefficient (N/m) |
C | Direct damping coefficient (N·s/m) |
c | Cross-coupled damping coefficient (N·s/m) |
M | Direct added mass (kg) |
m | Cross-coupled added mass (kg) |
f | Whirl frequency ratio |
References
- Lei, C.; Yiyang, Z.; Zhengwei, W.; Yexiang, X.; Ruixiang, L. Effect of Axial Clearance on the Efficiency of a Shrouded Centrifugal Pump. J. Fluids Eng. 2015, 137, 071101. [Google Scholar] [CrossRef]
- Zhou, W.; Qiu, N.; Wang, L.; Gao, B.; Liu, D. Dynamic Analysis of a Planar Multi-Stage Centrifugal Pump Rotor System Based on a Novel Coupled Model. J. Sound Vib. 2018, 434, 237–260. [Google Scholar] [CrossRef]
- Zhou, W.; Yu, D.; Wang, Y.; Shi, J.; Gan, B. Research on the Fluid-induced Excitation Characteristics of the Centrifugal Pump Considering the Compound Whirl Effect. Facta Univ. Ser. Mech. Eng. 2021. [Google Scholar] [CrossRef]
- Li, Y.; Wang, Y.; Dai, X.; Wang, Z. Sensitivity of different sealing structures to axial movement of centrifugal pump impeller. J. Drain Irrig Mach Eng. 2021, 39, 122–127. [Google Scholar] [CrossRef]
- Feng, J.; Wang, L.; Yang, H.; Peng, X. Numerical Investigation on the Effects of Structural Parameters of Labyrinth Cavity on Sealing Performance. Math. Probl. Eng. 2018, 2018, 5273582. [Google Scholar] [CrossRef]
- Cao, H.; Zhang, W.; Yin, L.; Yang, L. Numerical Study of Leakage and Rotordynamic Performance of Staggered Labyrinth Seals Working with Supercritical Carbon Dioxide. Shock Vib. 2022, 2022, 3896212. [Google Scholar] [CrossRef]
- Lee, S.I.; Kang, Y.J.; Kim, W.J.; Kwak, J.S.; Kim, T.S.; Kim, D.H.; Jung, I.Y. Effects of Tip Clearance, Number of Teeth, and Tooth Front Angle on the Sealing Performance of Straight and Stepped Labyrinth Seals. J. Mech. Sci. Technol. 2021, 35, 1539–1547. [Google Scholar] [CrossRef]
- Hur, M.S.; Lee, S.I.; Moon, S.W.; Kim, T.S.; Kwak, J.S.; Kim, D.H.; Jung, I.Y. Effect of Clearance and Cavity Geometries on Leakage Performance of a Stepped Labyrinth Seal. Processes 2020, 8, 1496. [Google Scholar] [CrossRef]
- Andrés, L.S.; Wu, T.; Barajas-Rivera, J.; Zhang, J.; Kawashita, R. Leakage and Cavity Pressures in an Interlocking Labyrinth Gas Seal: Measurements Versus Predictions. J. Eng. Gas Turbines Power 2019, 141, 101007. [Google Scholar] [CrossRef]
- Zhang, M.; Yang, J.; Xu, W.; Xia, Y. Leakage and Rotordynamic Performance of a Mixed Labyrinth Seal Compared with That of a Staggered Labyrinth Seal. J. Mech. Sci. Technol. 2017, 31, 2261–2277. [Google Scholar] [CrossRef]
- Woo, S.; Jang, H.; Kwak, H.; Moon, Y.; Kim, C. Leakage Analysis of Helical Grooved Pump Seal Using CFD. J. Mech. Sci. Technol. 2020, 34, 4183–4191. [Google Scholar] [CrossRef]
- Wróblewski, W.; Fraczek, D.; Marugi, K. Leakage Reduction by Optimisation of the Straight–through Labyrinth Seal with a Honeycomb and Alternative Land Configurations. Int. J. Heat Mass Transf. 2018, 126, 725–739. [Google Scholar] [CrossRef]
- Szymański, A.; Wróblewski, W.; Bochon, K.; Majkut, M.; Strozik, M.; Marugi, K. Experimental Validation of Optimised Straight-through Labyrinth Seals with Various Land Structures. Int. J. Heat Mass Transf. 2020, 158, 119930. [Google Scholar] [CrossRef]
- Wu, T.; Andrés, L.S. Gas Labyrinth Seals: Improved Prediction of Leakage in Gas Labyrinth Seals Using an Updated Kinetic Energy Carry-Over Coefficient. J. Eng. Gas Turbines Power 2020, 142, 121012. [Google Scholar] [CrossRef]
- Dogu, Y.; Sertçakan, M.C.; Bahar, A.S.; Pişkin, A.; Arıcan, E.; Kocagül, M. Computational Fluid Dynamics Investigation of Labyrinth Seal Leakage Performance Depending on Mushroom-Shaped Tooth Wear. J. Eng. Gas Turbines Power 2016, 138, 032503. [Google Scholar] [CrossRef]
- Li, Z.; Li, J.; Yan, X.; Feng, Z. Effects of Pressure Ratio and Rotational Speed on Leakage Flow and Cavity Pressure in the Staggered Labyrinth Seal. J. Eng. Gas Turbines Power 2011, 133, 114503. [Google Scholar] [CrossRef]
- Joachimiak, D.; Krzyśłak, P. Analysis of the Gas Flow in a Labyrinth Seal of Variable Pitch. J. Appl. Fluid Mech. 2019, 12, 921–930. [Google Scholar] [CrossRef]
- Nagai, K.; Koiso, K.; Kaneko, S.; Taura, H.; Watanabe, Y. Numerical and Experimental Analyses of Static and Dynamic Characteristics for Partially Helically Grooved Liquid Annular Seals. J. Tribol. 2019, 141, 022201. [Google Scholar] [CrossRef]
- Li, Z.; Li, J.; Feng, Z. Numerical Comparisons of Rotordynamic Characteristics for Three Types of Labyrinth Gas Seals with Inlet Preswirl. Proc. Inst. Mech. Eng. Part J. Power Energy 2016, 230, 721–738. [Google Scholar] [CrossRef]
- Zhang, W.; Gu, Q.; Wang, T. Study on the Rotordynamic Performance of a Novel Anti-Stagnation Labyrinth Seal. J. Vib. Eng. Technol. 2020, 8, 835–846. [Google Scholar] [CrossRef]
- Alex Moreland, J.; Childs, D.W.; Bullock, J.T. Measured Static and Rotordynamic Characteristics of a Smooth-Stator/Grooved-Rotor Liquid Annular Seal. J. Fluids Eng. 2018, 140, 101109. [Google Scholar] [CrossRef]
- Zhang, M.; Childs, D.W.; Tran, D.L.; Shresth, H. Effects of Clearance on the Performance of a Labyrinth Seal Under Wet-Gas Conditions. J. Eng. Gas Turbines Power 2020, 142, 111012. [Google Scholar] [CrossRef]
- Li, Z.; Li, J.; Feng, Z. Numerical Comparison of Rotordynamic Characteristics for a Fully Partitioned Pocket Damper Seal and a Labyrinth Seal With High Positive and Negative Inlet Preswirl. J. Eng. Gas Turbines Power 2016, 138, 042505. [Google Scholar] [CrossRef]
- Zhang, W.; Gu, Q.; Cao, H.; Wang, Y.; Yin, L. Improving the Rotordynamic Stability of Short Labyrinth Seals Using Positive Preswirl. J. Vibroengineering 2020, 22, 1295–1308. [Google Scholar] [CrossRef]
- Untaroiu, A.; Jin, H.; Fu, G.; Hayrapetiau, V.; Elebiary, K. The Effects of Fluid Preswirl and Swirl Brakes Design on the Performance of Labyrinth Seals. J. Eng. Gas Turbines Power 2018, 140, 082503. [Google Scholar] [CrossRef]
- Wu, T.; San Andrés, L. Pump Grooved Seals: A Computational Fluid Dynamics Approach to Improve Bulk-Flow Model Predictions. J. Eng. Gas Turbines Power 2019, 141, 101005. [Google Scholar] [CrossRef]
- Zhai, L.; Wu, G.; Wei, X.; Qin, D.; Wang, L. Theoretical and Experimental Analysis for Leakage Rate and Dynamic Characteristics of Herringbone-Grooved Liquid Seals. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 2015, 229, 849–860. [Google Scholar] [CrossRef]
- Zhai, L.; Zhenjie, Z.; Zhonghuang, C.; Jia, G. Dynamic Analysis of Liquid Annular Seals with Herringbone Grooves on the Rotor Based on the Perturbation Method. R. Soc. Open Sci. 2018, 5, 180101. [Google Scholar] [CrossRef] [PubMed]
- Zhai, L.; Chi, Z.; Guo, J.; Zhang, Z.; Zhu, Z. Theoretical Solutions for Dynamic Characteristics of Liquid Annular Seals with Herringbone Grooves on the Stator Based on Bulk-Flow Theory. Sci. Technol. Nucl. Install. 2018, 2018, 1–13. [Google Scholar] [CrossRef]
- Jia, X.; Zheng, Q.; Jiang, Y.; Zhang, H. Leakage and Rotordynamic Performance of T Type Labyrinth Seal. Aerosp. Sci. Technol. 2019, 88, 22–31. [Google Scholar] [CrossRef]
- Zhou, W.; Zhao, Z.; Wang, Y.; Shi, J.; Gan, B.; Li, B.; Qiu, N. Research on Leakage Performance and Dynamic Characteristics of a Novel Labyrinth Seal with Staggered Helical Teeth Structure. Alex. Eng. J. 2021, 60, 3177–3187. [Google Scholar] [CrossRef]
- Zhang, E.; Jiao, Y.; Chen, Z. Dynamic Behavior Analysis of a Rotor System Based on a Nonlinear Labyrinth-Seal Forces Model. J. Comput. Nonlinear Dyn. 2018, 13, 101002. [Google Scholar] [CrossRef]
- Tsukuda, T.; Hirano, T.; Watson, C.; Morgan, N.R.; Weaver, B.K.; Wood, H.G. A Numerical Investigation of the Effect of Inlet Preswirl Ratio on Rotordynamic Characteristics of Labyrinth Seal. J. Eng. Gas Turbines Power 2018, 140, 082506. [Google Scholar] [CrossRef]
- Rotordynamic Characteristics of Rotating Labyrinth Gas Turbine Seal with Centrifugal Growth. Tribol. Int. 2016, 97, 349–359. [CrossRef]
- Iwatsubo, T.; Ishimaru, H. Consideration of Whirl Frequency Ratio and Effective Damping Coefficient of Seal. J. Syst. Des. Dyn. 2010, 4, 177–188. [Google Scholar] [CrossRef] [Green Version]
Seal Parameters | Z | Cr (mm) | Hs (mm) | Hr (mm) | Hv (mm) | Bs (mm) | Bc (mm) | Br (mm) | Lp (mm) | L (mm) | D (mm) | θ (°) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Value | 4 | 0.3 | 2.7 | 1 | 0.3 | 1 | 3 | 1 | 1 | 18.5 | 50 | 45 |
Numerical Parameters/Details | Specification |
---|---|
Rotation speed | 1450 rpm |
Inlet pressure | 0.2 MPa |
Outlet pressure | 0 MPa |
Wall properties | Smooth, adiabatic, no-slip |
Turbulence model | Standard k-ε |
Wall function | Scalable |
Discretization | 2nd order upwind scheme |
Working medium | Clear water |
Tilt Angle θ (°) | Rotation Speed ω (rpm) | K (N/mm) | k (N/mm) | C (N·s/m) | c (N·s/m) |
---|---|---|---|---|---|
45 | 1000 | −55.03 | −0.17 | 12.08 | −0.74 |
2000 | −55.45 | −0.92 | 12.47 | −1.66 | |
3000 | −56.15 | −1.86 | 12.72 | −2.59 | |
70 | 1000 | −21.82 | 4.23 | 11.72 | −0.94 |
2000 | −22.06 | 7.77 | 12.42 | −2.01 | |
3000 | −22.69 | 11.81 | 13.19 | −3.15 | |
90 | 1000 | −10.23 | 3.83 | 9.28 | −0.95 |
2000 | −10.40 | 7.12 | 10.06 | −2.12 | |
3000 | −10.88 | 11.20 | 11.14 | −3.09 | |
135 | 1000 | 0.72 | 0.63 | −5.79 | −1.19 |
2000 | 0.62 | 0.62 | −4.84 | −2.19 | |
3000 | −0.14 | 0.35 | −3.63 | −3.16 |
Clearance Cr (mm) | Rotation Speed ω (rpm) | K (N/mm) | k (N/mm) | C (N·s/m) | c (N·s/m) |
---|---|---|---|---|---|
0.1 | 1000 | −23.99 | 22.93 | 14.07 | −1.08 |
2000 | −25.88 | 28.36 | 15.40 | −2.56 | |
3000 | −28.71 | 33.83 | 15.89 | −4.04 | |
0.3 | 1000 | −55.03 | −0.17 | 12.08 | −0.74 |
2000 | −55.45 | −0.92 | 12.47 | −1.66 | |
3000 | −56.15 | −1.86 | 12.72 | −2.59 | |
0.5 | 1000 | −26.07 | −1.50 | 8.18 | −0.51 |
2000 | −26.64 | −2.71 | 8.28 | −1.15 | |
3000 | −26.16 | −1.68 | 8.43 | −0.60 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Su, H.; Shi, J.; Zhou, W. Study on Leakage Performance and Rotordynamic Characteristics of a Novel Semi-Y Type Labyrinth Seal. Lubricants 2022, 10, 234. https://doi.org/10.3390/lubricants10100234
Su H, Shi J, Zhou W. Study on Leakage Performance and Rotordynamic Characteristics of a Novel Semi-Y Type Labyrinth Seal. Lubricants. 2022; 10(10):234. https://doi.org/10.3390/lubricants10100234
Chicago/Turabian StyleSu, Huihao, Junlin Shi, and Wenjie Zhou. 2022. "Study on Leakage Performance and Rotordynamic Characteristics of a Novel Semi-Y Type Labyrinth Seal" Lubricants 10, no. 10: 234. https://doi.org/10.3390/lubricants10100234