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The spatial-temporal sequence of velocity fields in wall turbulence with and without polymer additives at the same Reynolds number are measured by time-resolved particle image velocimetry (TRPIV) from the side and top views. Based on this experimental database of a water channel, the mechanism of drag reduction by polymers is explored from the viewpoint of the influence of polymer solution on the transport of momentum and energy in a turbulent boundary layer. Comparison of Reynolds stress profiles confirms that due to the existence of polymer additives, the transport of turbulent momentum is significantly inhibited, as if caused by the decrease of Reynolds shear stress. Furthermore, it is noted that these changes are closely related to the effect of polymer additives on the classical coherent structures, such as vortices and low-speed streaks, which are the dominant structures in near-wall turbulence. The spatial topological mode of hairpin vortex extracted by conditional sampling method shows that the intensity of vortices and ejection event are greatly suppressed by the polymer solution. Not only does the decline of turbulent kinetic energy production indicate that the energy of hairpin vortices that comes from the ensemble average movement is attenuated in the solution, but all this implys that the polymer additives hinder the self-sustaining mechanism, the inherent character of wall turbulence. Then, the analysis of linear stochastic estimation (LSE) suggests that the development of hairpin vortices in the packet is impeded, which is mainly reflected in the reduction of the number of hairpin vortices and the suppression of uplift in the wall-normal direction. To investigate the change of low-speed streaks after the addition of polymers, the spanwise autocorrelation function of streamwise fluctuating velocities has been calculated. In the polymer solution the large-scale vortices areflenhanced while the small-scale vortices are suppressed. This observation refleals that the polymers disrupt the energy transport from large to small scales. To summarize, it is through the action on coherent structures that the polymer additives can damp the transport of momentum and energy between the near-wall region and outer region of the boundary layer. In this way, the polymer solution makes turbulent flow less chaotic, leading to the reduction of friction drag.
[1] Toms B A 1948 Proceedings of the 1st International Congress on Rheology North Holland p135
[2] Lumley J L 1969 Annu. Rev. Fluid Mech. 1 367
[3] Hinch E J 1977 Phys. Fluids 20 22
[4] Ryskin G 1987 Phys. Rev. Lett. 59 2059
[5] Tabor M, de Gennes P G 1986 Europhys. Lett. 2 519
[6] Sreenivasan K R, White C M 2000 J. Fluid Mech. 409 149
[7] Dimitropoulos C D, Sureshkumar R, Beris A N, Handler R A 2001 Phys. Fluids 13 1016
[8] De Angelis E, Casciola C M, Piva R 2002 Comput. Fluids 31 495
[9] Chemloul N S 2014 Energy 64 818
[10] Shao X M, Lin J Z, Wu T Li Y L 2002 Can J. Chem Eng 80 293
[11] Kim K, Adrian R J Balachandar S, Sureshkumar R 2008 Phys Rev. Lett 100 134504
[12] Motozawa M, Ishitsuka S, Iwamoto K, Ando H, Senda T, Kawaguchi Y 2012 Flow Turbul. Combust 88 121
[13] Guan X L, Yao S Y, Jiang N 2013 Acta Mech. Sin. 29 485
[14] Kenis P R 1971 J Appl Polym Sci 15 607
[15] Hinze J O (translated by Zhou G J et al.) 1987 Turbulence (Vol.2) (Beijing: Science Press) p298 (in Chinese) [Hinze J O著 (周光炯等译) 1987 湍流 (下册) (北京: 科学出版社) 第298页]
[16] Luchik T S, Tiederman W G 1988 J. Fluid Mech. 190 241
[17] Fan X, Jiang N 2005 Mechanics in Engineering 27 28 (in Chinese) [樊星, 姜楠 2005 力学与实践 27 28]
[18] Robinson S K 1991 Annu. Rev. Fluid Mech. 23 601
[19] Sibilla S, Beretta C P 2005 Fluid Dyn Res 37 183
[20] Cai W H, Li F C, Zhang H N 2011 Chin. Phys. B 20 124702
[21] Li F C, Cai W H, Zhang H N, Wang Y 2012 Chin. Phys. B 21 114701
[22] Kchemann D 1965 J. Fluid Mech. 21 1
[23] Zhou J, Adrian R J, Balachandar S, Kendall T M 1999 J. Fluid Mech. 387 353
[24] Jiang N, Guan X L, Yu P N 2012 Chinese Journal of Theoretical and Applied Mechanics 44 213 (in Chinese) [姜楠, 管新蕾, 于培宁 2012 力学学报 44 213]
[25] Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703
[26] Adrian R J, Christensen K T, Liu Z C 2000 Exp. Fluids 29 275
[27] Adrian R J, Meinhart C D, Tomkins C D 2000 J. Fluid Mech. 422 1
[28] Willmarth W W, Lu S S 1972 J. Fluid Mech. 55 65
[29] Swearingen J D, Blackwelder R F 1987 J. Fluid Mech. 182 255
[30] Kim K, Li C F, Sureshkumar R, Balachandar S, Adrian R J 2007 J Fluid Mech 584 281
[31] Zhang Z S, Cui G X, Xu C X 2005 Turbulence Theory and Simulation (Beijing: Tsinghua University Press) p17 (in Chinese) [张兆顺, 崔桂香, 许春晓 2005 湍流理论与模拟 (北京: 清华大学出版社) 第17页]
[32] Johansson A V, Alfredsson P H, Kim J 1991 J Fluid Mech 224 579
[33] Zhou J, Adrian R J Balachandar S 1996 Phys. Fluids 8 288
[34] Chen L, Tang D B, Liu C Q 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌, 刘超群 2011 60 094702]
[35] Adrian R J 1994 Appl. Sci. Res. 53 291
[36] Tomkins C D, Adrian R J 2003 J. Fluid Mech. 490 37
[37] Christensen K T, Adrian R J 2001 J. Fluid Mech. 431 433
[38] Kline S J, Reynolds W C, Schraub F A, Runstadler P W 1967 J. Fluid Mech. 30 741
[39] White C M, Somandepalli V S R, Mungal M G 2004 Exp. Fluids 36 62
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[1] Toms B A 1948 Proceedings of the 1st International Congress on Rheology North Holland p135
[2] Lumley J L 1969 Annu. Rev. Fluid Mech. 1 367
[3] Hinch E J 1977 Phys. Fluids 20 22
[4] Ryskin G 1987 Phys. Rev. Lett. 59 2059
[5] Tabor M, de Gennes P G 1986 Europhys. Lett. 2 519
[6] Sreenivasan K R, White C M 2000 J. Fluid Mech. 409 149
[7] Dimitropoulos C D, Sureshkumar R, Beris A N, Handler R A 2001 Phys. Fluids 13 1016
[8] De Angelis E, Casciola C M, Piva R 2002 Comput. Fluids 31 495
[9] Chemloul N S 2014 Energy 64 818
[10] Shao X M, Lin J Z, Wu T Li Y L 2002 Can J. Chem Eng 80 293
[11] Kim K, Adrian R J Balachandar S, Sureshkumar R 2008 Phys Rev. Lett 100 134504
[12] Motozawa M, Ishitsuka S, Iwamoto K, Ando H, Senda T, Kawaguchi Y 2012 Flow Turbul. Combust 88 121
[13] Guan X L, Yao S Y, Jiang N 2013 Acta Mech. Sin. 29 485
[14] Kenis P R 1971 J Appl Polym Sci 15 607
[15] Hinze J O (translated by Zhou G J et al.) 1987 Turbulence (Vol.2) (Beijing: Science Press) p298 (in Chinese) [Hinze J O著 (周光炯等译) 1987 湍流 (下册) (北京: 科学出版社) 第298页]
[16] Luchik T S, Tiederman W G 1988 J. Fluid Mech. 190 241
[17] Fan X, Jiang N 2005 Mechanics in Engineering 27 28 (in Chinese) [樊星, 姜楠 2005 力学与实践 27 28]
[18] Robinson S K 1991 Annu. Rev. Fluid Mech. 23 601
[19] Sibilla S, Beretta C P 2005 Fluid Dyn Res 37 183
[20] Cai W H, Li F C, Zhang H N 2011 Chin. Phys. B 20 124702
[21] Li F C, Cai W H, Zhang H N, Wang Y 2012 Chin. Phys. B 21 114701
[22] Kchemann D 1965 J. Fluid Mech. 21 1
[23] Zhou J, Adrian R J, Balachandar S, Kendall T M 1999 J. Fluid Mech. 387 353
[24] Jiang N, Guan X L, Yu P N 2012 Chinese Journal of Theoretical and Applied Mechanics 44 213 (in Chinese) [姜楠, 管新蕾, 于培宁 2012 力学学报 44 213]
[25] Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703
[26] Adrian R J, Christensen K T, Liu Z C 2000 Exp. Fluids 29 275
[27] Adrian R J, Meinhart C D, Tomkins C D 2000 J. Fluid Mech. 422 1
[28] Willmarth W W, Lu S S 1972 J. Fluid Mech. 55 65
[29] Swearingen J D, Blackwelder R F 1987 J. Fluid Mech. 182 255
[30] Kim K, Li C F, Sureshkumar R, Balachandar S, Adrian R J 2007 J Fluid Mech 584 281
[31] Zhang Z S, Cui G X, Xu C X 2005 Turbulence Theory and Simulation (Beijing: Tsinghua University Press) p17 (in Chinese) [张兆顺, 崔桂香, 许春晓 2005 湍流理论与模拟 (北京: 清华大学出版社) 第17页]
[32] Johansson A V, Alfredsson P H, Kim J 1991 J Fluid Mech 224 579
[33] Zhou J, Adrian R J Balachandar S 1996 Phys. Fluids 8 288
[34] Chen L, Tang D B, Liu C Q 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌, 刘超群 2011 60 094702]
[35] Adrian R J 1994 Appl. Sci. Res. 53 291
[36] Tomkins C D, Adrian R J 2003 J. Fluid Mech. 490 37
[37] Christensen K T, Adrian R J 2001 J. Fluid Mech. 431 433
[38] Kline S J, Reynolds W C, Schraub F A, Runstadler P W 1967 J. Fluid Mech. 30 741
[39] White C M, Somandepalli V S R, Mungal M G 2004 Exp. Fluids 36 62
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