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Effects of the slip wall on the drag and coherent structures of turbulent boundary layer

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Abstract

A comparative experiment by time-resolved particle image velocimetry (TRPIV) of the turbulent boundary layer (TBL) over a smooth surface and an anisotropy superhydrophobic (SH) surface was carried out in an open-surface recirculating water channel at \(Re_{\tau ,smooth}= 650\). The wall friction velocity is fitted well from the velocity of the viscous sublayer calculated by the Single-pixel resolution ensemble correlation (SPEC). After that, a drag reduction rate of 17%, a slip velocity of 0.0119 m/s, and a slip length of \(90.8\,{\upmu }\hbox {m}\) are obtained over the SH surface. In the main modes of the reduced-order flow fields, the wave packet structures over the SH surface become “upright”. Such large-scale structures in motion are also found in the instantaneous field. According to the statistical results of the correlation, it is found that the slip wall leads to the change of the convection velocity at different positions of the structure, which leads to the change of structure morphology and the distortion of the shear layer.

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References

  1. Lu, L., Li, D., Gao, Z., et al.: Characteristics of array of distributed synthetic jets and effect on turbulent boundary layer. Acta. Mech. Sin. 36(6), 1171–1190 (2020). https://doi.org/10.1007/s10409-020-01001-x

    Article  MathSciNet  Google Scholar 

  2. Cui, X., Jiang, N., Zheng, X., et al.: Active control of multiscale features in wall-bounded turbulence. Acta. Mech. Sin. 36(1), 12–21 (2020). https://doi.org/10.1007/s10409-019-00907-5

    Article  MathSciNet  Google Scholar 

  3. Park, H., Sun, G., Kim, C.J.C.: Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722–734 (2014). https://doi.org/10.1017/jfm.2014.151

    Article  Google Scholar 

  4. Hu, H., Wen, J., Bao, L., et al.: Significant and stable drag reduction with air rings confined by alternated superhydrophobic and hydrophilic strips. Sci. Adv. 3(9), e1603288 (2017). https://doi.org/10.1126/sciadv.1603288

    Article  Google Scholar 

  5. Wang, D., Sun, Q., Hokkanen, M.J., et al.: Design of robust superhydrophobic surfaces. Nature 582(7810), 55–59 (2020). https://doi.org/10.1038/s41586-020-2331-8

    Article  Google Scholar 

  6. Min, T.G., Kim, J.: Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16(7), L55–L58 (2004). https://doi.org/10.1063/1.1755723

    Article  MATH  Google Scholar 

  7. Woolford, B., Prince, J., Maynes, D., et al.: Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21(8), 085106 (2009). https://doi.org/10.1063/1.3213607

    Article  MATH  Google Scholar 

  8. Jelly, T.O., Jung, S.Y., Zaki, T.A.: Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26(9), 1–8 (2014)

    Article  Google Scholar 

  9. Busse, A., Sandham, N.D.: Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24(5), 055111 (2012). https://doi.org/10.1063/1.4719780

    Article  Google Scholar 

  10. Ling, H., Srinivasan, S., Golovin, K., et al.: High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670–703 (2016). https://doi.org/10.1017/jfm.2016.450

    Article  MathSciNet  MATH  Google Scholar 

  11. Abu Rowin, W., Ghaemi, S.: Streamwise and spanwise slip over a superhydrophobic surface. J. Fluid Mech. 870, 1127–1157 (2019). https://doi.org/10.1017/jfm.2019.225

    Article  MathSciNet  MATH  Google Scholar 

  12. Fairhall, C.T., Abderrahaman-Elena, N., Garcí a-Mayoral, R.: The effect of slip and surface texture on turbulence over superhydrophobic surfaces. J. Fluid Mech. 861, 88–118 (2018). https://doi.org/10.1017/jfm.2018.909

    Article  MathSciNet  MATH  Google Scholar 

  13. Watanabe, K., Udagawa, H.: Brag reduction of non-Newtonian fluids in a circular pipe with a highly water-repellent wall. AIChE J. 47(2), 256–262 (2001). https://doi.org/10.1002/aic.690470204

    Article  Google Scholar 

  14. Ou, J., Rothstein, J.P.: Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17(10), 103606 (2005). https://doi.org/10.1063/1.2109867

    Article  MATH  Google Scholar 

  15. Choi, C.H., Ulmanella, U., Kim, J., et al.: Effective slip and friction reduction in nanograted superhydrophobic microchannels. Phys. Fluids 18(8), 087105 (2006). https://doi.org/10.1063/1.2337669

    Article  Google Scholar 

  16. Joseph, P., Cottin-Bizonne, C., Benoit, J.M., et al.: Slippage of water past superhydrophobic carbon nanotube forests in microchannels. Phys. Rev. Lett. 97(15), 156104 (2006). https://doi.org/10.1103/PhysRevLett.97.156104

    Article  Google Scholar 

  17. Jung, Y.C., Bhushan, B.: Biomimetic structures for fluid drag reduction in laminar and turbulent flows. J. Phys. 22(3), 035104 (2010). https://doi.org/10.1088/0953-8984/22/3/035104

    Article  Google Scholar 

  18. Bixler, G.D., Bhushan, B.: Bioinspired micro/nanostructured surfaces for oil drag reduction in closed channel flow. Soft Matter 9(48), 11709 (2013)

    Google Scholar 

  19. Daniello, R.J., Waterhouse, N.E., Rothstein, J.P.: Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21(8), 085103 (2009). https://doi.org/10.1063/1.3207885

    Article  MATH  Google Scholar 

  20. Bidkar, R.A., Leblanc, L., Kulkarni, A.J., et al.: Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces. Phys. Fluids 26(8), 085108 (2014). https://doi.org/10.1063/1.4892902

    Article  Google Scholar 

  21. Tian, H., Zhang, J., Jiang, N., et al.: Effect of hierarchical structured superhydrophobic surfaces on coherent structures in turbulent channel flow. Exp. Thermal Fluid Sci. 69, 27–37 (2015). https://doi.org/10.1016/j.expthermflusci.2015.07.018

    Article  Google Scholar 

  22. Gose, J.W., Golovin, K., Boban, M., et al.: Characterization of superhydrophobic surfaces for drag reduction in turbulent flow. J. Fluid Mech. 845, 560–580 (2018). https://doi.org/10.1017/jfm.2018.210

    Article  MathSciNet  MATH  Google Scholar 

  23. Park, H., Park, H., Kim, J.: A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25(11), 110815 (2013). https://doi.org/10.1063/1.4819144

    Article  Google Scholar 

  24. Rastegari, A., Akhavan, R.: On the mechanism of turbulent drag reduction with super-hydrophobic surfaces. J. Fluid Mech. 773, R4 (2015). https://doi.org/10.1017/jfm.2015.266

    Article  Google Scholar 

  25. Westerweel, J., Geelhoed, P.F., Lindken, R.: Single-pixel resolution ensemble correlation for micro-PIV applications. Exp. Fluids 37(3), 375–384 (2004). https://doi.org/10.1007/s00348-004-0826-y

    Article  Google Scholar 

  26. Shen, J.Q., Pan, C., Wang, J.J.: Accurate measurement of wall skin friction by single-pixel ensemble correlation. Sci. China Phys. Mech. 57(7), 1352–1362 (2014). https://doi.org/10.1007/s11433-014-5462-9

    Article  Google Scholar 

  27. Towne, A., Schmidt, O.T., Colonius, T.: Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867 (2018). https://doi.org/10.1017/jfm.2018.283

    Article  MathSciNet  MATH  Google Scholar 

  28. Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010). https://doi.org/10.1017/s0022112010001217

    Article  MathSciNet  MATH  Google Scholar 

  29. Jovanovic, M.R., Schmid, P.J., Nichols, J.W.: Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26(2), 024103 (2014). https://doi.org/10.1063/1.4863670

    Article  Google Scholar 

  30. de Brederode, V., Bradshaw, P.: Influence of the side walls on the turbulent center-plane boundary-layer in a square duct. J. Fluids Eng. 100(1), 91–96 (1978). https://doi.org/10.1115/1.3448621

    Article  Google Scholar 

  31. Araya, G., Castillo, L., Hussain, F.: The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers. J. Fluid Mech. 775, 189–200 (2015). https://doi.org/10.1017/jfm.2015.296

    Article  MathSciNet  MATH  Google Scholar 

  32. Abu Rowin, W., Ghaemi, S.: Effect of Reynolds number on turbulent channel flow over a superhydrophobic surface. Phys. Fluids 32(7), 075105 (2020). https://doi.org/10.1063/5.0012584

    Article  Google Scholar 

  33. Deng, S., Pan, C., Wang, J., et al.: On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number. J. Fluid Mech. 844, 635–668 (2018). https://doi.org/10.1017/jfm.2018.160

    Article  MathSciNet  MATH  Google Scholar 

  34. Balakumar, B.J., Adrian, R.J.: Large- and very-large-scale motions in channel and boundary-layer flows. Philos. Trans. R. Soc. A 365(1852), 665–681 (2007). https://doi.org/10.1098/rsta.2006.1940

    Article  MATH  Google Scholar 

  35. Wang, H.P., Wang, S.Z., He, G.W.: The spanwise spectra in wall-bounded turbulence. Acta. Mech. Sin. 34(3), 452–461 (2018). https://doi.org/10.1007/s10409-017-0731-2

    Article  Google Scholar 

  36. Adrian, R.J.: Hairpin vortex organization in wall turbulence. Phys. Fluids 19(4), 041301 (2007). https://doi.org/10.1063/1.2717527

    Article  MATH  Google Scholar 

  37. Christensen, K.T., Adrian, R.J.: Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443 (2001). https://doi.org/10.1017/S0022112001003512

    Article  MATH  Google Scholar 

  38. Yao, Y.C., Huang, W.X., Xu, C.X.: Amplitude modulation and extreme events in turbulent channel flow. Acta. Mech. Sin. 34(1), 1–9 (2018). https://doi.org/10.1007/s10409-017-0687-2

    Article  Google Scholar 

  39. Zhao, X., He, G.W.: Space-time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79(4), 046316 (2009). https://doi.org/10.1103/PhysRevE.79.046316

    Article  Google Scholar 

  40. Wang, W., Guan, X.L., Jiang, N.: Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry. Chin. Phys. B 23(10), 104703 (2014). https://doi.org/10.1088/1674-1056/23/10/104703

    Article  Google Scholar 

  41. Christensen, K., Wu, Y.: Characteristics of vortex organization in the outer layer of wall turbulence. 4th International Symposium on Turbulence and Shear Flow Phenomena 3, 1025–1030 (2005)

    Google Scholar 

  42. Volino, R.J., Schultz, M.P., Flack, K.A.: Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293 (2007). https://doi.org/10.1017/s0022112007008518

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11732010, 11572221, 11872272, U1633109, 11802195) and the National Key R&D Program of the Ministry of Science and Technology, China, on “Green Buildings and Building Industrialization” (Grant 2018YFC0705300).

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Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Tianjin, 300354, China

    Xinwei Wang, Yufei Wang & Nan Jiang

  2. National Demonstration Center for Experimental Mechanics Education, Taiyuan University of Technology, Taiyuan, 030024, China

    Haiping Tian

  3. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin, 300354, China

    Nan Jiang

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  1. Xinwei Wang
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Correspondence to Nan Jiang.

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Executive Editor: Jinjun Wang.

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Wang, X., Wang, Y., Tian, H. et al. Effects of the slip wall on the drag and coherent structures of turbulent boundary layer. Acta Mech. Sin. 37, 1278–1290 (2021). https://doi.org/10.1007/s10409-021-01092-0

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