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Tomographic TR-PIV measurement of coherent structure spatial topology utilizing an improved quadrant splitting method

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Abstract

In this paper, we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry. An improved quadrant splitting method, based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique, was introduced as a criterion to detect the coherent structure topology. Furthermore, we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event (Q2) or a fourth-quadrant event (Q4). Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction, compared to the one in the other two directions. The relationship among such topological coherent structures and Reynolds stress bursting events, as well as the fluctuating vorticity was discussed. When other burst events are surveyed (the first-quadrant event Q1 and the third-quadrant event Q3), a fascinating bursting period circularly occurs: Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction. In addition, the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence. The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed, which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.

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References

  1. Kline S J, Reynolds W C, Schraub F A, et al. The structure of turbulent boundary layers. J Fluid Mech, 1967, 30(4): 741–773

    Article  ADS  Google Scholar 

  2. Robinson S K. Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech, 1991, 23(1): 601–639

    Article  ADS  Google Scholar 

  3. Yang S Q, Jiang N. Wavelet analysis to detect multi-scale coherent eddy structures and intermittency in turbulent boundary layer. In: Proceedings of the eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’11). Shanghai: IEEE, 2011. 1241–1245

    Chapter  Google Scholar 

  4. Cantwell B J. Organized motion in turbulent flow. Annu Rev Fluid Mech, 1981, 13(1): 457–515

    Article  MathSciNet  ADS  Google Scholar 

  5. Hussain A. Coherent structures and turbulence. J Fluid Mech, 1986, 173(1): 303–356

    Article  ADS  Google Scholar 

  6. Theodorsen T. Mechanism of turbulence. In: Proceedings of the 2nd Midwestern Conference on Fluid Mechanics. Columbus, Ohio: Ohio State University, 1952. 1–18

    Google Scholar 

  7. Perry A E, Chong M S. On the mechanism of wall turbulence. J Fluid Mech, 1982, 119(1): 173–217

    Article  ADS  MATH  Google Scholar 

  8. Adrian R J, Meinhart C D, Tomkins C D. Vortex organization in the outer region of the turbulent boundary layer. J Fluid Mech, 2000, 422(1): 1–54

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Balakumar B J, Adrian R J. Large-and very-large-scale motions in channel and boundary-layer flows. Philos Trans R Soc Lond Ser A-Math Phys Eng Sci, 2007, 365(1852): 665–681

    Article  ADS  MATH  Google Scholar 

  10. Panton R L. Overview of the self-sustaining mechanisms of wall turbulence. Prog Aerosp Sci, 2001, 37(4): 341–384

    Article  Google Scholar 

  11. Elsinga G, Kuik D, Van Oudheusden B, et al. Investigation of the three-dimensional coherent structures in a turbulent boundary layer with Tomographic-PIV. In: Proceedings of 45th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada: AIAA, 2007. 1305

    Google Scholar 

  12. Lu S S, Willmarth W W. Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J Fluid Mech, 1973, 60(3): 481–511

    Article  ADS  Google Scholar 

  13. Sun K H, Shu W. On the burst detection techniques in wall-turbulence (in Chinese). Chin J Theor Appl Mech. 1994, 26(4): 488–493

    MathSciNet  Google Scholar 

  14. Schröder A, Geisler R, Elsinga G E, et al. Investigation of a turbulent Spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids, 2008, 44(2): 305–316

    Article  Google Scholar 

  15. Schröder A, Geisler R, Staack K, et al. Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids, 2011: 1–21

  16. Yang S Q, Jiang N. On the measurement of spatial characteristic scale in turbulent boundary layer based on tomographic time-resolved PIV (in Chinese). J Exp Mech, 2011, 26(04): 369–376

    Google Scholar 

  17. Jiang N, Zhang J. Detecting multi-scale coherent eddy structures and intermittency in turbulent boundary layer by wavelet analysis. Chin Phys Lett, 2005, 22: 1968–1971

    Article  MathSciNet  ADS  Google Scholar 

  18. Farge M, Schneider K. Coherent Vortex Simulation (CVS), a semideterministic turbulence model using wavelets. Flow Turbul Combust, 2001, 66(4): 393–426

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu W, Jiang N. Three kinds of velocity structure function in turbulent flows. Chin Phys Lett, 2004, 21: 1989–1992

    Article  ADS  Google Scholar 

  20. Liu J H, Jiang N, Wang Z D, et al. Multi-scale coherent structures in turbulent boundary layer detected by locally averaged velocity structure functions. Appl Math Mech, 2005, 26(4): 495–504

    Article  MathSciNet  MATH  Google Scholar 

  21. Tang Z Q, Jiang N. TR PIV experimental investigation on bypass transition induced by a cylinder wake. Chin Phys Lett, 2011, 28: 054702

    Article  ADS  Google Scholar 

  22. Tomkins C D, Adrian R J. Spanwise structure and scale growth in turbulent boundary layers. J Fluid Mech, 2003, 490: 37–74

    Article  ADS  MATH  Google Scholar 

  23. Schoppa W, Hussain F. Coherent structure generation in near-wall turbulence. J Fluid Mech, 2002, 453: 57–108

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China

    ShaoQiong Yang & Nan Jiang

  2. State Key Laboratory of Non-linear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China

    Nan Jiang

  3. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin, 300072, China

    Nan Jiang

Authors
  1. ShaoQiong Yang
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  2. Nan Jiang
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Correspondence to Nan Jiang.

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Yang, S., Jiang, N. Tomographic TR-PIV measurement of coherent structure spatial topology utilizing an improved quadrant splitting method. Sci. China Phys. Mech. Astron. 55, 1863–1872 (2012). https://doi.org/10.1007/s11433-012-4887-2

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  • DOI: https://doi.org/10.1007/s11433-012-4887-2

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