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Drag reduction by riblets has drawn the attention of many researchers because of its low production cost and easy maintenance. But due to the fact that the rather low drag reduction riblets can offered, an easy modification to the structure of riblets to improve the performance would be more than necessary. In this work, an investigation of the influences on coherent structure of straight riblets and sinusoidal riblets (s-riblets) in a turbulent boundary layer (TBL) at various Reynolds numbers is carried out experimentally by using the time-resolved particle image velocimetry (TR-PIV). It is found that the skin friction of the turbulent boundary layer is reduced close to the wall, and the logarithmic velocity profile shifts upwards over riblets and s-riblets. The turbulence intensity and Reynolds shear stress are also reduced in the near wall region compared with the scenario of the smooth case, and a better performance on drag reduction is obtained over s-riblets. Coherent structures including hairpin vortex and low speed streaks are extracted over test plates by using the correlation coefficient and
$\lambda_{ci}$ vortex identification method, to study the mechanism of drag reduction caused by riblets. It is shown that the spatial scale of coherent structure in streamwise and wall-normal direction decrease over riblets and s-riblets to various degrees, the inclination angle between the mainstream and coherent structure also decreases, meaning that the wall-normal movement and upwash motion are suppressed over riblets and s-riblets. Results from the conditional sampling method demonstrate that the induction of ejection and sweep motions by hairpin vortex are inhibited over riblets and hence the exchange of energy and momentum and the self-sustaining mechanism in turbulence are influenced. Furthermore, at the same$Re_{\tau}$ , the spanwise spacing of low speed streaks turns wider with wall-normal position increasing. At the same$ y^{+} $ , a larger spacing is seen over riblets and s-riblets, implying that spanwise movement of the streaks is restrained and hence becomes more stable.-
Keywords:
- wall bounded turbulence /
- drag reduction /
- coherent structure /
- sinusoidal riblets
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Google Scholar
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Google Scholar
[21] El-Samni O A, Chun H H, Yoon H S 2007 Int. J. Eng. Sci. 45 436
Google Scholar
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Google Scholar
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Google Scholar
[44] 李山, 杨绍琼, 姜楠 2013 力学学报 02 183
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[53] Kline S J, Reynolds W C, Schraub F A, Runstadler P W 1967 J. Fluid Mech. 30 741
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Google Scholar
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图 1 实验模型示意图 (a) 光滑平板; (b) 传统直线型沟槽板; (c) 正弦波型沟槽板
Figure 1. Schematic diagram of experimental plates: (a) Smooth plate; (b) riblets; (c) s-riblets
图 2 正弦波沟槽截面图 (a) 左视图; (b) 俯视图
Figure 2. Cross section of s-riblets: (a) Left view; (b) top view
图 3 实验装置示意图 (a) case 1; (b) case 2
Figure 3. Schematic diagram of experimental setup: (a) case 1; (b) case 2.
图 4 不同壁面流场的流向平均速度剖面
Figure 4. Mean velocity profiles in TBL flows over test plates
图 5 不同壁面流场湍流度的分布曲线
Figure 5. Distribution of turbulent intensities over test plates
图 6 不同壁面流场雷诺切应力的分布曲线
Figure 6. Distribution of Reynolds shear stress over test plates
图 7 不同壁面流场流向脉动速度在
$x-y$ 平面内的相关系数Figure 7. Correlation coefficients of the streamwise fluctuation in
$x-y$ plane over test plates
图 9
$x-y$ 平面条件平均相干结构 (上)$y^{+}$ = 71.1; (下)$y^{+}$ = 128Figure 9. Conditionally-averaged structure in the
$x-y$ plane: (top)$y^{+}$ = 71.1; (bottom)$y^{+}$ = 128
图 11
$x-z$ 平面内不同壁面上流场$y^{+}$ = 9.7流向脉动速度云图Figure 11. Instantaneous streamwise fluctuating velocity in
$x-z$ plane at$y^{+}$ = 9.7
图 12 不同壁面上流场
$u'$ 沿展向的自相关函数Figure 12. Autocorrelation function of
$u'$ in the$z$ -direction over test plates表 1 湍流边界层基本参数及减阻率
Table 1. Basic parameters and results for turbulent boundary layers over test plates.
工况 $U_{e}$ /m·s–1 $\delta$/$\rm mm$ $Re_{\tau}$ $u_{\tau}$/cm·s–1 $\tau_{w}$/$\rm kg\cdot(m\cdot s^{2})^{-1}$ $C_{f}$ $DR$/% 平板 0.1 70.2 337.8 0.4713 0.02216 0.004442 0 2D沟槽 0.1 71.6 337.1 0.4611 0.02121 0.004252 4.29 S-沟槽 0.1 71.6 336 0.4596 0.02108 0.004224 4.87 平板 0.2 66.4 661.4 0.9756 0.09497 0.004759 0 2D沟槽 0.2 67.8 645.3 0.9322 0.08671 0.004345 8.70 S-沟槽 0.2 68.5 648.1 0.9266 0.08566 0.004293 9.80 
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[1] Christensen K T, Adrian R J 2001 J. Fluid Mech. 431 433
Google Scholar
[2] Adrian R J 2007 Phys. Fluids 19 41301
Google Scholar
[3] Eitel-Amor G, Örlü R, Schlatter P, Flores OAdrian R J 2015 Phys. Fluids 27 25108
Google Scholar
[4] Lu S S, Willmarth W W 1973 J. Fluid Mech. 60 481
Google Scholar
[5] Choi K 1989 J. Fluid Mech. 208 417
Google Scholar
[6] Orlandi P, Jiménez J 1994 Phys. Fluids 6 634
Google Scholar
[7] Bechert D W, Bruse M, Hage W, Meyer R 2000 Naturwissenschaften 87 157
Google Scholar
[8] Bixler G D, Bhushan B 2013 Adv. Funct. Mater. 23 4507
Google Scholar
[9] Dean B, Bhushan B 2010 Philos. Trans. R. Soc. A 368 4775
Google Scholar
[10] Walsh M J 1982 AIAA 20th Aerospace Sciences Meeting Orlando Florida, January 11-14, 1982 p169
[11] Walsh M J, M. L A 1984 AIAA 22th Aerospace Sciences Meeting Reno Nevada, January 9-12, 1984 p347
[12] Djenidi L, Anselmet F, Liandrat J, Fulachier L 1994 Phys. Fluids 6 2993
Google Scholar
[13] Raayai-Ardakani S, Mckinley G H 2017 Phys. Fluids 29 93605
Google Scholar
[14] Haecheon C, Parviz M, John K 1991 Phys. Fluids A 3 1892
[15] Grek G R, Kozlov V V, Titarenko S V, Klingmann B G B 1995 Phys. Fluids 7 2504
Google Scholar
[16] Arthur G K, Haecheon C, Parviz M 1993 Phys. Fluids A 3307
[17] Bechert D W, Bruse M, Hage W, van der Hoeven J G T, Hoppe G 1997 J. Fluid Mech. 338 59
Google Scholar
[18] Yang S, Li S, Tian H, Wang Q, Jiang N 2016 Acta Mech. Sin. Prc. 32 284
Google Scholar
[19] Walsh M J 1983 AIAA J. 21 485
[20] Goldstein D, Handler R, Sirovich L 1995 J. Fluid Mech. 302 333
Google Scholar
[21] El-Samni O A, Chun H H, Yoon H S 2007 Int. J. Eng. Sci. 45 436
Google Scholar
[22] Goldstein D B, Tuan T C 1998 J. Fluid Mech. 363 115
Google Scholar
[23] García-Mayoral R and Jiménez J 2011 J. Fluid Mech. 678 317
Google Scholar
[24] Lee S J, Lee S H 2001 Exp. Fluids 153
[25] Suzuki Y, Kasagi N 1994 AIAA J. 32 1781
Google Scholar
[26] Choi H, Moin P, Kim J 1993 J. Fluid Mech. 255 503
Google Scholar
[27] Viswanath P R 2002 Prog. Aerosp. Sci. 38 571
Google Scholar
[28] García-Mayoral R, Jiménez J 2011 Philos. Trans. R. Soc. A 369 1412
Google Scholar
[29] Stenzel V, Wilke Y, Hage W 2011 Prog. Org. Coat. 70 224
Google Scholar
[30] Wassen E, Kramer F, Thiele F, Grüeneberger R, Hage W, Meyer R 2008 AIAA 4th Flow Control Conference Seattle Washington, June 23-26, 2008 p4204
[31] Grüneberger R, Kramer F, Wassen E, Hage W, Meyer R, Thiele F 2012 Nature-Inspired Fluid Mechanics (Berlin: Springer) P311
[32] Quadrio M, Luchini 1768 US Patent 057 662
[33] Hagiwara H C F R 2013 J. Bioeng. 10 341
Google Scholar
[34] Peet Y, Sagaut P 2008 38th AIAA Fluid Dynamics Conference and Exhibit Seattle Washington, June 23-26, 2008 p3745
[35] Peet Y, Sagaut P, Charron Y 2009 Int. J. Hydrogen Energy 34 8964
Google Scholar
[36] Peet Y, Sagaut P 2009 Phys. Fluids 21 105105
Google Scholar
[37] Adiran R J, Westerwell J 2011 Particle Image Velocimetry (Cambridge: Cambridge University Press)
[38] Tang Z Q, Jiang N 2012 Exp. Fluids 53 343
Google Scholar
[39] Prasad A K, Adrian R J, Landreth C C, Offutt P W 1992 Exp. Fluids 105
[40] Hooshmand D, Youngs R, M W J 1983 AIAA-paper 0230 0230
[41] Bechert D W, Bartenwerfer M 1989 J. Fluid Mech. 206 105
Google Scholar
[42] 樊星, 姜楠 2005 力学与实践 27 28
Google Scholar
Fan X, Jiang N 2005 Mech. Eng. 27 28
Google Scholar
[43] Wang J, Lan S, Chen G 2000 Fluid Dyne. Res. 27 217
Google Scholar
[44] 李山, 杨绍琼, 姜楠 2013 力学学报 02 183
Google Scholar
Li S, Yang S, Jiang N 2013 Chin. J. Theor. Appl. Mech. 02 183
Google Scholar
[45] Jiménez J 2018 J. Fluid Mech. 842 1
Google Scholar
[46] Chen J, Hussain F, Pei J, She Z 2014 J. Fluid Mech. 742 291
Google Scholar
[47] Farano M, Cherubini S, De Palma P, Robinet J C 2018 Eur. J. Mech. B-Fluid 72 74
Google Scholar
[48] Perlin M, Steven D R D 2016 J. Fluids Eng. 138 091104
Google Scholar
[49] Jiménez J, Pinelli A 1999 J. Fluid Mech. 389 335
Google Scholar
[50] Zhou J, Adrian R J, Balachandar S, Kendall T M 1999 J. Fluid Mech. 387 353
Google Scholar
[51] Adrian R J, Meinhart C D, Tomkins C D 2000 J. Fluid Mech. 422 1
Google Scholar
[52] Li S, Jiang N, Yang S, Huang Y, Wu Y 2018 Chin. Phys. B 27 104701
Google Scholar
[53] Kline S J, Reynolds W C, Schraub F A, Runstadler P W 1967 J. Fluid Mech. 30 741
Google Scholar
[54] Nakagawa H, Nezu I 1981 J. Fluid Mech. 104 1
Google Scholar
[55] Smith C R, Metzler S P 1983 J. Fluid Mech. 129 27
Google Scholar
[56] Choi K S 2013 A. M. R. 745 27
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