On the Comparison of Liutex Method with Other Vortex Identification Methods in a Confined Tip-Leakage Cavitating Flow

  • Conference paper
  • First Online:
Liutex and Third Generation of Vortex Definition and Identification

Abstract

In the current paper, Large Eddy Simulation on the confined tip leakage cavitating flow generated by a straight NACA0009 hydrofoil with a clearance size gap = 10 mm is performed. TLV cavitation and TSV cavitation are reasonably captured. Different vortex identification methods of all three generations, including vorticity, Q-criterion, Ω method and Liutex method are compared in detail with the simulated tip leakage cavitating results. It is observed that the Ω method and the Liutex method, show advantages in visualizing vortical structures in the currently studied flow regime with a strong capability in filtering out shearing contaminations. Both Liutex vector field and Liutex iso-surface show potentials in investigating vortical cavitating flow. Differences of cavitating and non-cavitating tip vortices mainly lie in their sizes and the generation of small-scale vortices around the TSV, which indicates the effect of cavitation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. X. Long et al., Large eddy simulation and Euler-Lagrangian coupling investigation of the transient cavitating turbulent flow around a twisted hydrofoil. Int. J. Multiphase Flow 100, 41–56 (2018)

    Article  MathSciNet  Google Scholar 

  2. X.-R. Bai et al., Large eddy simulation of tip leakage cavitating flow focusing on cavitation-vortex interaction with Cartesian cut-cell mesh method. J. Hydrodynam. 30(4), 750–753 (2018)

    Article  ADS  Google Scholar 

  3. C.-C. Wang et al., Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods. J. Hydrodynam. 31(3), 475–494 (2019)

    Article  ADS  Google Scholar 

  4. R.E.A. Arndt, Cavitation in fluid machinery and hydraulic structures. Annu. Rev. Fluid Mech. 13, 273–328 (1981)

    Article  ADS  Google Scholar 

  5. J. Katz, Cavitation phenomena within regions of flow separation. J. Fluid Mech. 140(MAR), 397–436 (1984)

    Article  ADS  Google Scholar 

  6. Q. Le, J.P. Franc, J.M. Michel, Partial cavities - global behavior and MEAN pressure distribution. J. Fluids Eng. Trans. Asme 115(2), 243–248 (1993)

    Article  Google Scholar 

  7. R.E.A. Arndt, Cavitation in vortical flows. Annu. Rev. Fluid Mech. 34(1), 143–175 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  8. Y.N. Zhang et al., A selected review of vortex identification methods with applications. J. Hydrodynam. 30(5), 767–779 (2018)

    Article  ADS  Google Scholar 

  9. C.Q. Liu et al., New omega vortex identification method. Sci. China Phys. Mech. Astron. 59(8), 9 (2016)

    Article  ADS  Google Scholar 

  10. C.Q. Liu et al., Rortex-a new vortex vector definition and vorticity tensor and vector decompositions. Phys. Fluids 30(3), 12 (2018)

    Article  Google Scholar 

  11. J. Liu, Y. Gao, C. Liu, An objective version of the Rortex vector for vortex identification. Phys. Fluids 31(6) (2019)

    Google Scholar 

  12. J. Liu, C. Liu, Modified normalized Rortex/vortex identification method. Phys. Fluids 31(6) (2019)

    Google Scholar 

  13. J.-M. Liu et al., Objective Omega vortex identification method. J. Hydrodynam. 31(3), 455–463 (2019)

    Article  ADS  Google Scholar 

  14. H. Xu, X.-s. Cai, C. Liu, Liutex (vortex) core definition and automatic identification for turbulence vortex structures. J. Hydrodynam. 31(5), 857–863 (2019)

    Article  ADS  Google Scholar 

  15. Y.-S. Gao et al., A Liutex based definition and identification of vortex core center lines. J. Hydrodynam. 31(3), 445–454 (2019)

    Article  ADS  Google Scholar 

  16. C.Q. Liu et al., Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. J. Hydrodynam. 31(2), 205–223 (2019)

    Article  ADS  Google Scholar 

  17. Y.-Q. Wang et al., Liutex theoretical system and six core elements of vortex identification. J. Hydrodynam. 32(2), 197–211 (2020)

    Article  ADS  Google Scholar 

  18. X.-D. Bai et al., The visualization of turbulent coherent structure in open channel flow. J. Hydrodynam. 31(2), 266–273 (2019)

    Article  ADS  Google Scholar 

  19. N. Gui et al., Analysis and correlation of fluid acceleration with vorticity and Liutex (Rortex) in swirling jets. J. Hydrodynam. 31(5), 864–872 (2019)

    Article  ADS  Google Scholar 

  20. L. Wang et al., Extension omega and omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow. J. Hydrodynam. 31(5), 911–921 (2019)

    Article  ADS  Google Scholar 

  21. X.R. Dong et al., POD analysis on vortical structures in MVG wake by Liutex core line identification. J. Hydrodynam. 32(3), 497–509 (2020)

    Article  ADS  Google Scholar 

  22. Y.-F. Wang et al., The applicability of vortex identification methods for complex vortex structures in axial turbine rotor passages. J. Hydrodynam. 31(4), 700–707 (2019)

    Article  ADS  Google Scholar 

  23. X. Bai et al., Comparative study of different vortex identification methods in a tip-leakage cavitating flow. Ocean Eng. 207 (2020)

    Google Scholar 

  24. J. Chen et al., Numerical investigation of the cavitating flow structure with special emphasis on the vortex identification method. Mod. Phys. Lett. B 34(4), 19 (2020)

    Article  MathSciNet  Google Scholar 

  25. R.E.A. Arndt, V.H. Arakeri, H. Higuchi, Some observations of tip-vortex cavitation. J. Fluid Mech. 229, 269–289 (1991)

    Article  ADS  Google Scholar 

  26. D.H. You et al., Study of tip-clearance flow in turbomachines using large-eddy simulation. Comput. Sci. Eng. 6(6), 38–46 (2004)

    Article  Google Scholar 

  27. B. Lakshminarayana, M. Pouagare, R. Davino, Three-dimensional flow field in the tip region of a compressor rotor passage—Part I: Mean velocity profiles and Annulus Wall boundary layer. J. Eng. Power 104(4), 760–771 (1982)

    Article  Google Scholar 

  28. K. Roussopoulos, P.A. Monkewitz, Measurements of tip Vortex characteristics and the effect of an anti-cavitation lip on a model Kaplan Turbine Blade. Flow. Turb. Combust. 64(2), 119 (2000)

    Article  Google Scholar 

  29. D. Bertetta et al., CPP propeller cavitation and noise optimization at different pitches with panel code and validation by cavitation tunnel measurements. Ocean Eng. 53, 177–195 (2012)

    Article  Google Scholar 

  30. A. Asnaghi, U. Svennberg, R.E. Bensow, Large Eddy simulations of cavitating tip vortex flows. Ocean Eng. 195, 26 (2020)

    Article  Google Scholar 

  31. H.Y. Cheng et al., Large eddy simulation of the tip-leakage cavitating flow with an insight on how cavitation influences vorticity and turbulence. App. Math. Model. 77, 788–809 (2020)

    Article  MathSciNet  Google Scholar 

  32. M. Dreyer et al., Mind the gap: a new insight into the tip leakage vortex using stereo-PIV. Exp. Fluids 55(11) (2014)

    Google Scholar 

  33. Q. Guo et al., Numerical simulation for the tip leakage vortex cavitation. Ocean Eng. 151, 71–81 (2018)

    Article  Google Scholar 

  34. H. Cheng et al., A new Euler-Lagrangian cavitation model for tip-vortex cavitation with the effect of non-condensable gas. Int. J. Multiphase Flow, 103441 (2020)

    Google Scholar 

  35. F. Nicoud, F. Ducros, Subgrid-scale stress Modelling based on the square of the velocity gradient tensor. Flow. Turb. Combust. 62(3), 183–200 (1999)

    Article  Google Scholar 

  36. P. Zwart, A.G. Gerber, T. Belamri, A two-phase flow model for predicting cavitation dynamics, in Fifth International Conference on Multiphase Flow, (2004)

    Google Scholar 

  37. J.C.R. Hunt, A.A. Wray, P. Moin, Eddies, Streams, and Convergence Zones in Turbulent Flows in Studying Turbulence Using Numerical Simulation Databases, (1988)

    Google Scholar 

  38. Y.S. Gao, C.Q. Liu, Rortex and comparison with eigenvalue-based vortex identification criteria. Phys. Fluids 30(8), 18 (2018)

    Article  Google Scholar 

  39. H.Y. Cheng et al., Suppressing tip-leakage vortex cavitation by overhanging grooves. Exp. Fluids 61(7), 18 (2020)

    Article  Google Scholar 

  40. P. Meunier, T. Leweke, Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533, 125–159 (2005)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Project nos. 51822903, 11772239, and 11772305). The numerical calculations in this paper were done on the supercomputing system in the Supercomputing Center of Wuhan University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Huaiyu Cheng .

Editor information

Editors and Affiliations

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bai, X., Cheng, H., Ji, B. (2021). On the Comparison of Liutex Method with Other Vortex Identification Methods in a Confined Tip-Leakage Cavitating Flow. In: Liu, C., Wang, Y. (eds) Liutex and Third Generation of Vortex Definition and Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-70217-5_8

Download citation

Publish with us

Policies and ethics

Navigation