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Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force

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Abstract

A formulation of the skin-friction drag related to the Reynolds shear stress in a turbulent channel flow is derived. A direct numerical simulation (DNS) of the turbulent control is performed by imposing the spatially oscillating spanwise Lorentz force. Under the action of the Lorentz force with several proper control parameters, only the periodically well-organized streamwise vortices are finally observed in the near-wall region. The Reynolds shear stress decreases dramatically, especially in the near-wall area, resulting in a drag reduction.

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References

  1. Theodorsen, T. Mechanism of turbulence. Proceedings of the 2nd Midwestern Conference on Fluid Mechanics, Ohio State University, Ohio, 1–18 (1952)

    Google Scholar 

  2. Kline, S. J., Reynolds, W. C., Schraub, F. A., and Runstadler, P. W. The structure of turbulent boundary layers. Journal of Fluid Mechanics, 30, 741–773 (1967)

    Article  Google Scholar 

  3. Cantwell, B. J. Organized motion in turbulent flow. Annual Review of Fluid Mechanics, 13, 457–515 (1981)

    Article  Google Scholar 

  4. Kim, J., Moin, P., and Moser, R. D. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal of Fluid Mechanics, 177, 133–166 (1987)

    Article  MATH  Google Scholar 

  5. Blackwelder, R. F. and Kaplan, R. E. On the wall structure of the turbulent boundary layer. Journal of Fluid Mechanics, 76, 89–112 (1976)

    Article  Google Scholar 

  6. Lee, C. B. and Wu, J. Z. Transition in wall-bounded flows. Applied Mechanics Reviews, 61, 030802 (2008)

  7. Lee, C. B. and Lee, R. Q. Dominant structure for turbulent production in a transitional boundary layer. Journal of Turbulence, 8, 1–34 (2007)

    Article  Google Scholar 

  8. Kim, J. and Bewley, T. R. A linear systems approach to flow control. Annual Review of Fluid Mechanics, 39, 383–417 (2007)

    Article  MathSciNet  Google Scholar 

  9. Kim, J. Physics and control of wall turbulence for drag reduction. Philosophical Transactions of the Royal Society, A: Mathematical, Physical and Engineering Sciences, 369, 1396–1411 (2011)

    Article  MATH  Google Scholar 

  10. Choi, K. Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Physics of Fluids, 14, 2530–2542 (2002)

    Article  Google Scholar 

  11. Ricco, P. and Wu, S. On the effects of later wall oscillation on a turbulent boundary layer. Experimental Thermal and Fluid Science, 29, 41–52 (2004)

    Article  Google Scholar 

  12. Quadrio, M., Ricco, P., and Viotti, C. Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. Journal of Fluid Mechanics, 627, 161–178 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kang, S. and Choi, H. Active wall motions for skin-friction drag reduction. Physics of Fluids, 12, 3301–3304 (2000)

    Article  Google Scholar 

  14. Endo, T., Kasagi, N., and Suzukin, Y. Feedback control of wall turbulence with wall deformation. International Journal of Heat and Fluid Flow, 21, 568–575 (2000)

    Article  Google Scholar 

  15. Shen, L., Zhang, X., Yue, K. P., and Triantafyllou, M. S. Turbulent flow over a flexible wall undergoing a streamwise traveling wave motion. Journal of Fluid Mechanics, 484, 197–221 (2003)

    Article  MATH  Google Scholar 

  16. Min, T., Kang, S. M., Speyer, J. L., and Kim, J. Sustained sub-laminar drag in a fully developed channel flow. Journal of Fluid Mechanics, 558, 309–318 (2006)

    Article  MATH  Google Scholar 

  17. Lee, C., Min, T., and Kim, J. Stability of channel flow subject to wall blowing and suction in the form of a traveling wave. Physics of Fluids, 20, 10153 (2008)

    Google Scholar 

  18. Zhang, H., Fan, B. C., Chen, Z. H., and Li, Y. L. Underlay mechanism in lift-drag phase diagrams for shear flow over cylinder. Applied Mathematics and Mechanics (English Edition), 35(2), 221–228 (2014) DOI 10.1007/s10483-014-1785-8

    Article  MathSciNet  Google Scholar 

  19. Zhu, Z. J., Niu, J. L., and Li, Y. L. Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers. Applied Mathematics and Mechanics (English Edition), 35(8), 959–978 (2014) DOI 10.1007/s10483-014-1847-7

    Article  MathSciNet  Google Scholar 

  20. Huang, L. P., Fan, B. C., and Dong, G. Turbulent drag reduction via a transverse wave travelling along streamwise direction induced by Lorentz force. Physics of Fluids, 22, 015103 (2010)

  21. Wu, W. T., Hong, Y. J., and Fan, B. C. Vortex structures in turbulent channel flow modulated by spanwise Lorentz force with steady distributions. Acta Physica Sinica, 63, 054702 (2014)

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Correspondence to Yanji Hong.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 11172140 and 11372356) and the Open Project of State Key Laboratory of Explosion Science and Technology in Beijing Institute of Technology (No.KFJJ13-3M)

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Wu, W., Hong, Y. & Fan, B. Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force. Appl. Math. Mech.-Engl. Ed. 36, 1113–1120 (2015). https://doi.org/10.1007/s10483-015-1972-6

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  • DOI: https://doi.org/10.1007/s10483-015-1972-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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