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Liutex (vorex) cores in transitional boundary layer with spanwise-wall oscillation

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Abstract

The vortex core detection method based on the Liutex vector is utilized to investigate the alternation of vortical structures on a boundary layer transition subjected to spanwise-wall oscillation. Compared with iso-surface based methods, the Liutex core line method is shown to be precise, free of threshold and capable to capture both strong and weak vortices simultaneously. Tollmien-Schlichting (T-S) waves in the linear growth region, Λ — and hairpin vortices in the transition region and twisted vortices in the turbulent region are all well captured by Liutex core lines. The cyclic wall movement accelerates the transition process while reducing the turbulent drag by 21.8% with selected parameters. For the wall oscillation case, the development from T-S wave to Λ — vortex is advanced about one T-S wave length in the streamwise direction. In the transition region, the Λ — vortex and legs of hairpin vortex are shortened in the wall oscillation case, and the symmetry of the vortical structures is lost in the late transition region since the introduction of asymmetry disturbances by the cyclic wall movement. Extrusions of weak vortices at the edge of boundary layer are found in the turbulent section which is often omitted by iso-surface based vortex identification method. Thus, it is demonstrated that for the transitional boundary layer the Liutex core line method provides a systematic and threshold-free vortex definition, which could serve as a powerful tool to understand and guide flow control.

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References

  1. Liu C., Gao Y. S., Dong X. R. et al. Third generation of vortex identification methods: Omega and Liutex/Rortex based systems [J]. Journal of Hydrodynamics, 2019, 31(2): 205–223.

    Article  Google Scholar 

  2. Liu C., Wang Y. Q., Yang Y. et al. New Omega vortex identification method [J]. Science China: Physics, Mechanics and Astronomy, 2016, 59(8): 684711.

    Google Scholar 

  3. Liu C., Gao Y., Tian S. et al. Rortex-A new vortex vector definition and vorticity tensor and vector decompositions [J]. Physics of Fluids, 2018, 30(3): 034103.

    Article  Google Scholar 

  4. Gao Y., Liu C. Rortex and comparison with eigenvalue-based vortex identification criteria [J]. Physics of Fluids, 2018, 30(8): 085107.

    Article  Google Scholar 

  5. Robinson S. K. Coherent motion in the turbulent boundary layer [J]. Annual Review of Fluid Mechanics, 1991, 23(1): 601–639.

    Article  Google Scholar 

  6. Wang Y., Yang Y., Yang G. et al. DNS study on vortex and vorticity in late boundary layer transition [J]. Communications in Computational Physics, 2017, 22: 441–459.

    Article  MathSciNet  Google Scholar 

  7. Chong M., Perry A., Cantwell B. A general classification of three dimensional flow fields [J]. Physics of Fluids A, 1990, 2(5): 765–777.

    Article  MathSciNet  Google Scholar 

  8. Hunt J., Wray A., Moin P. Eddies, streams, and convergence zones in turbulent flows [R]. Proceedings of the Summer Program. Stanford, CA, USA: Center for Turbulence Research, 1988, 193–208.

    Google Scholar 

  9. Zhou J., Adrian R., Balachandar S. et al. Mechanisms for generating coherent packets of hairpin vortices in channel flow [J]. Journal of Fluid Mechanics, 1999, 387: 252–296.

    Article  MathSciNet  MATH  Google Scholar 

  10. Jeong J., Hussain F. On the identification of a vortex [J]. Journal of Fluid Mechanics, 1995, 285: 69–94.

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang Y. Q., Gao Y. S., Liu J. M. et al. Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition [J]. Journal of Hydrodynamics, 2019, 31(3): 464–474.

    Article  Google Scholar 

  12. Gao Y. Q., Liu J. M., Yu Y. F. et al. A Liutex based definition of vortex rotation axis line [J]. Journal of Hydrodynamics, 2019, 31(3): 445–454.

    Article  Google Scholar 

  13. Xu H., Cai X. S., Liu C. Liutex (vortex) core definition and automatic identification for turbulence vortex structures [J]. Journal of Hydrodynamics, 2019, 31(5): 857–863.

    Article  Google Scholar 

  14. Jung J., Mangiavacchin N., Akhavan R. Suppression of turbulence in wall spanwise oscillations [J]. Physics of Fluids A: Fluid Dynamics, 1992, 4(8): 1605–1607.

    Article  Google Scholar 

  15. Baron A., Quadrio M. Turbulent drag reduction by spanwise wall oscillations [J]. Applied Scientific Research, 1995, 55(4): 311–326.

    Article  MATH  Google Scholar 

  16. Quadrio M., Ricco P. Initial response of a turbulent channel flow to spanwise oscillation of the walls [J]. Journal of Turbulence, 2003, 4: N7.

    Article  Google Scholar 

  17. Xu C., Huang W. Transient response of Reynolds stress transport to spanwise wall oscillation in a turbulent channel flow [J]. Physics of Fluids, 2005, 17(1): 018101.

    Article  MATH  Google Scholar 

  18. Choi K. S. Near-wall structure of turbulent boundary layer with spanwise-wall oscillation [J]. Physics of Fluids, 2002, 14: 2530.

    Article  MATH  Google Scholar 

  19. Karniadakis G. E., Choi K. S. Mechanisms on transverse motions in turbulent wall flows [J]. Annual Review of Fluid Mechanics, 2003, 35: 45–62.

    Article  MathSciNet  MATH  Google Scholar 

  20. Trujillo S., Bogard D., Ball K. et al. Turbulent boundary layer drag reduction using an oscillating wall [C]. 4th Shear Flow Control Conference, Snowmass Village, Colorado, USA, 1997.

  21. Dhanak M. R., Si C. On reduction of turbulent wall friction through spanwise wall oscillations [J]. Journal of Fluid Mechanics, 1999, 383: 175–195.

    Article  MATH  Google Scholar 

  22. Quadrio M., Ricco P. Critical assessment of turbulent drag reduction through spanwise wall oscillations [J]. Journal of Fluid Mechanics, 2004, 521: 251–271.

    Article  MATH  Google Scholar 

  23. Choi K. S., Clayton B. R. The mechanism of turbulent drag reduction with wall oscillation [J]. International Journal of Heat and Fluid Flow, 2001, 22(1): 1–9.

    Article  Google Scholar 

  24. Quadrio M., Ricco P., Viotti C. Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction [J]. Journal of Fluid Mechanics, 2009, 627: 161–178.

    Article  MathSciNet  MATH  Google Scholar 

  25. Yudhistira I., Skote M. Direct numerical simulation of a turbulent boundary layer over an oscillating wall [J]. Journal of Turbulence, 2011, 12: N9.

    Article  Google Scholar 

  26. Skote M. Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall [J]. International Journal of Heat and Fluid Flows, 2012, 38: 1–12.

    Article  Google Scholar 

  27. Wallace J. M. Highlights from 50 years of turbulent boundary layer research [J]. Journal of Turbulence, 2013, 13: 1.

    Google Scholar 

  28. Durcros F., Comte P., Lesieur M. Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate [J]. Journal of Fluid Mechanics, 1996, 326: 1–36.

    Article  MATH  Google Scholar 

  29. Ricco P., Wu S. On the effects of lateral wall oscillations on a turbulent boundary layer [J]. Experimental Thermal and Fluid Science, 2004, 29(1): 41–52.

    Article  Google Scholar 

  30. Wang Y., Al-Dujaly H., Yan Y. et al. Physics of multiple level hairpin vortex structures in turbulence [J]. Science China: Physics, Mechanics and Astronomy, 2016, 59(2): 624703.

    Google Scholar 

  31. Zhang Y. N., Liu K. H., Li J. W. et al. Analysis of the vortices in the inner flow of reversible pump turbine with the new omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30(3): 463–469.

    Article  Google Scholar 

  32. Gui N., Ge L., Cheng P. X. et al. Comparative assessment and analysis of rorticity by Rortex in swirling jets [J]. Journal of Hydrodynamics, 2019, 31(3): 495–503.

    Article  Google Scholar 

  33. Wang C. C., Liu Y., Chen J. et al. Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods [J]. Journal of Hydrodynamics, 2019, 31(3): 475–494.

    Article  Google Scholar 

  34. Wang L., Zheng Z. Y., Cai W. H. et al. Extension Omega and Omega-Liutex methods to the identification of vortex structures in viscoelastic turbulent flow [J]. Journal of Hydrodynamics, 2019, 31(5): 911–921.

    Article  Google Scholar 

  35. Wang Y. F., Zhang W. H., Cao X. et al. A discussion on the applicability of vortex identification methods for complex vortex structures in axial turbine rotor passages [J]. Journal of Hydrodynamics, 2019, 31(4): 700–707.

    Article  Google Scholar 

  36. Liu C., Yan Y., Lu P. Physics of turbulence generation and sustence in a transitional boundary layer [J]. Computers and Fluids, 2014, 102: 353–384.

    Article  Google Scholar 

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Acknowledgments

The work was supported by the European Commission and Ministry of Industry and Information Technology (MIIT) of China through the Research and Innovation action DRAGY (Grant No. 690623). This investigation is accomplished by using code DNSUTA developed by Dr. Chaoqun Liu at the University of Texas at Arlington. We also thank Prof. Hongyi Xu from Fudan University for providing the executable files to automatically detect Liutex core lines. Helpful discussions with Prof. Lian-di Zhou are highly appreciated by the authors.

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Authors and Affiliations

  1. School of Mathematical Science, Soochow University, Suzhou, 215006, China

    Yi-qian Wang

  2. Department of Mathematics, University of Texas at Arlington, Arlington, 76019, USA

    Chaoqun Liu

Authors
  1. Yi-qian Wang
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  2. Chaoqun Liu
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Corresponding author

Correspondence to Chaoqun Liu.

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 11702159).

Biography: Yi-qian Wang (1987-), Male, Ph. D., Associate Professor

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Wang, Yq., Liu, C. Liutex (vorex) cores in transitional boundary layer with spanwise-wall oscillation. J Hydrodyn 31, 1178–1189 (2019). https://doi.org/10.1007/s42241-019-0092-3

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  • DOI: https://doi.org/10.1007/s42241-019-0092-3

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