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

doi:10.1007/s10483-019-2471-7

Abstract

Abstract:

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, composite materials, laminated plates, dynamic stability, electromagnetic force, turbulent channel flow, drag reduction

2010 MSC Number:

Daiwen JIANG, Hui ZHANG, Baochun FAN, Zijie ZHAO, Jian LI, Mingyue GUI. Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 435-448.

TrendMD

References

[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)
[2] TANG, Z. Q., JIANG, N., ZHENG, X. B., and WU, Y. H. Bursting process of large-and smallscale structures in turbulent boundary layer perturbed by a cylinder roughness element. Experiments in Fluids, 57(5), 1-14(2016)
[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)
[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) https://doi.org/10.1007/s10483-014-1785-8
[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)
[6] LIM, J., CHOI, H., and KIM, J. Control of streamwise vortices with uniform magnetic fluxes. Physics of Fluids, 10, 1997-2005(1998)
[7] JIMÉNEZ, J. and PINELLI, A. The autonomous cycle of near-wall turbulence. Journal of Fluid Mechanics, 389, 335-359(2000)
[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)
[9] DU, Y. Q. and KARNIADAKIS, G. E. Suppressing wall turbulence by means of a transverse traveling wave. Science, 288, 1230-1234(2000)
[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)
[11] LEE, C. and KIM, J. Control of the viscous sublayer for drag reduction. Physics of Fluids, 14, 2523-2529(2002)
[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)
[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)
[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)
[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)
[16] OSTILLAMÓNICO, R. and LEE, A. A. Controlling turbulent drag across electrolytes using electric fields. Faraday Discussions, 199, 159-173(2017)
[17] ALTINTA?, 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)
[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)
[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)
[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) https://doi.org/10.1007/s10483-015-1972-6
[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)
[22] SCHOPPA, W. and HUSSAIN, F. Coherent structure dynamics in near-wall turbulence. Fluid Dynamics Research, 26, 119-139(2000)
[23] SCHOPPA, W. and HUSSAIN, F. Coherent structure generation in near-wall turbulence. Journal of Fluid Mechanics, 453, 57-108(2002)