Applied Mathematics and Mechanics

, Volume 40, Issue 4, pp 435–448 | Cite as

Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers

  • Daiwen Jiang
  • Hui ZhangEmail author
  • Baochun Fan
  • Zijie Zhao
  • Jian Li
  • Mingyue Gui


In this paper, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with the direct numerical simulation (DNS) methods for different Reynolds numbers. A formulation is derived to express the relation between the drag and the Reynolds shear stress. With the application of optimal electromagnetic force, the in-depth relations among characteristic structures in the flow field, mean Reynolds shear stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The regular quasi-streamwise vortex structures, which appear in the flow field, have the same period with that of the electromagnetic force. These structures suppress the random velocity fluctuations, which leads to the absolute value of mean Reynolds shear stress decreasing and the distribution of that moving away from the wall. Moreover, the wave number of optimal electromagnetic force increases, and the scale of the regular quasi-streamwise vortex structures decreases as the Reynolds number increases. Therefore, the rate of drag reduction decreases with the increase in the Reynolds number since the scale of the regular quasi-streamwise vortex structures decreases.

Key words

flow control drag reduction electromagnetic force turbulent channel flow 

Chinese Library Classification


2010 Mathematics Subject Classification

76D55 76F70 76W05 


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  1. [1]
    HU, H. B., WEN, J., BAO, L. Y., JIA, L. B., SONG, D., SONG, B. W., PAN, G., SCARAGGI, M., DINI, D., XUE, Q. J., and ZHOU, F. Significant and stable drag reduction with air rings confined by alternated superhydrophobic and hydrophilic strips. Science Advances, 3, e1603288 (2017)CrossRefGoogle Scholar
  2. [2]
    TANG, Z. Q., JIANG, N., ZHENG, X. B., and WU, Y. H. Bursting process of large- and small-scale structures in turbulent boundary layer perturbed by a cylinder roughness element. Experiments in Fluids, 57(5), 1–14 (2016)CrossRefGoogle Scholar
  3. [3]
    FENG, L. H., CHOI, K. S., and WANG, J. J. Flow control over an airfoil using virtual Gurney flaps. Journal of Fluid Mechanics, 767, 595–626 (2015)CrossRefGoogle Scholar
  4. [4]
    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(8), 959–978 (2014) MathSciNetCrossRefGoogle Scholar
  5. [5]
    AUTERI, F., BARON, A., BELAN, M., CAMPANARDI, G., and QUADRIO, M. Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow. Physics of Fluids, 22, 115103 (2010)CrossRefGoogle Scholar
  6. [6]
    LIM, J., CHOI, H., and KIM, J. Control of streamwise vortices with uniform magnetic fluxes. Physics Of Fluids, 10, 1997–2005 (1998)CrossRefGoogle Scholar
  7. [7]
    JIMÉNEZ, J. and PINELLI, A. The autonomous cycle of near-wall turbulence. Journal of Fluid Mechanics, 389, 335–359 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    SATAKE, S. I. and KASAGI, N. Turbulence control with wall-adjacent thin layer damping spanwise velocity fluctuations. International Journal of Heat & Fluid Flow, 17, 343–352 (1996)CrossRefGoogle Scholar
  9. [9]
    DU, Y. Q. and KARNIADAKIS, G. E. Suppressing wall turbulence by means of a transverse traveling wave. Science, 288, 1230–1234 (2000)CrossRefGoogle Scholar
  10. [10]
    DU, Y. Q., SYMEONIDIS, V., and KARNIADAKIS, G. E. Drag reduction in wall-bounded turbulence via a transverse travelling wave. Journal of Fluid Mechanics, 457, 1–34 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    LEE, C. and KIM, J. Control of the viscous sublayer for drag reduction. Physics of Fluids, 14, 2523–2529 (2002)CrossRefzbMATHGoogle Scholar
  12. [12]
    QUADRIO, M., RICCO, P., and VIOTTI, C. Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction. Journal of Fluid Mechanics, 627, 161–178 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    VIOTTI, C., QUADRIO, M., and LUCHINI, P. Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction. Physics of Fluids, 21, 105109 (2009)CrossRefzbMATHGoogle Scholar
  14. [14]
    MOUBARAK, L. M. and ANTAR, G. Y. Dynamics of a two-dimensional flow subject to steady electromagnetic forces. Experiments in Fluids, 53, 1627–1636 (2012)CrossRefGoogle Scholar
  15. [15]
    HABCHI, C. and ANTAR, G. The dynamics of two-dimensional turbulence excited at two scales using electromagnetic forces. Physics of Fluids, 28, 005102 (2016)Google Scholar
  16. [16]
    OSTILLAMÓNICO, R. and LEE, A. A. Controlling turbulent drag across electrolytes using electric fields. Faraday Discussions, 199, 159–173 (2017)CrossRefGoogle Scholar
  17. [17]
    ALTINTAŞ;, A. and DAVIDSON, L. Direct numerical simulation analysis of spanwise oscillating Lorentz force in turbulent channel flow at low Reynolds number. Acta Mechanica, 228, 1–18 (2016)MathSciNetGoogle Scholar
  18. [18]
    HUANG, L. P., FAN, B. C., and DONG, G. Turbulent drag reduction via a transverse wave traveling along streamwise direction induced by Lorentz force. Physics of Fluids, 22, 015103 (2010)CrossRefzbMATHGoogle Scholar
  19. [19]
    HUANG, L. P., CHOI, K. S., FAN, B. C., and CHEN, Y. H. Drag reduction in turbulent channel flow using bidirectional wavy Lorentz force. Science China Physics, Mechanics & Astronomy, 57, 2133–2140 (2014)CrossRefGoogle Scholar
  20. [20]
    WU, W. T., HONG, Y. J., and FAN, B. C. Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force. Applied Mathematics and Mechanics (English Edition), 36(9), 1113–1120 (2015) MathSciNetCrossRefGoogle Scholar
  21. [21]
    KIM, J., MOIN, P., and MOSER, R. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal of Fluid Mechanics, 177, 133–166 (1987)CrossRefzbMATHGoogle Scholar
  22. [22]
    SCHOPPA, W. and HUSSAIN, F. Coherent structure dynamics in near-wall turbulence. Fluid Dynamics Research, 26, 119–139 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    SCHOPPA, W. and HUSSAIN, F. Coherent structure generation in near-wall turbulence. Journal of Fluid Mechanics, 453, 57–108 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Daiwen Jiang
    • 1
  • Hui Zhang
    • 1
    • 2
    Email author
  • Baochun Fan
    • 1
  • Zijie Zhao
    • 1
  • Jian Li
    • 1
  • Mingyue Gui
    • 1
  1. 1.Science and Technology on Transient Physics LaboratoryNanjing University of Science and TechnologyNanjingChina
  2. 2.Department of MathematicsImperial College LondonLondonUK

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