正弦波沟槽对湍流边界层相干结构影响的TR-PIV实验研究

李山; 姜楠; 杨绍琼

doi:10.7498/aps.68.20181875

摘要

利用高时间分辨率粒子图像测速(time-resolved particle image velocimetry, TR-PIV)技术, 在不同雷诺数下对光滑壁面和二维顺流向、三维正弦波(two/three dimensional, 2D/3D)沟槽壁面湍流边界层流场进行了实验测量, 从不同沟槽对湍流边界层相干结构影响的角度分析了其减阻的机理. 对比不同壁面的各阶统计量结果发现: 沟槽降低了壁面摩擦阻力, 存在减阻效果, 正弦波沟槽的减阻率增大. 运用相关函数、$\lambda_{ci}$检测准则等方法提取了不同壁面湍流边界层发卡涡和低速条带等典型相干结构的空间拓扑形态, 结果表明: 两种沟槽壁面的相干结构在流向和法向上的空间尺度均有不同程度的减小, 且相干结构与主流之间的倾角趋于更小, 流体在法向上的运动及结构的抬升受到明显抑制, 发卡涡诱导喷射和扫掠的能力降低, 从而影响了湍流中能量与动量的输运过程及湍流的自维持机制, 且相比于2D沟槽, 3D正弦波沟槽作用效果更为明显. 在同一雷诺数下, 随着距离壁面法向位置的增加, 不同壁面湍流边界层低速条带的展向间距都变宽; 但同一法向位置处2D/3D沟槽壁面湍流边界层低速条带的间距与光滑壁面的相比更宽, 沟槽的存在有效抑制了低速条带在展向上的运动, 使得低速条带更稳定.

关键词:

Abstract

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:

作者及机构信息

1.
天津大学机械工程学院, 天津　300072

2.
青岛海洋科学与技术试点国家实验室, 青岛　266237

通信作者: 姜楠, nanj@tju.edu.cn ; 杨绍琼, shaoqiongy@tju.edu.cn

基金项目: 国家自然科学基金(批准号: 11732010, 11572221, 11872272, U1633109, 11802195)、国家重点研发计划(批准号: 2018YFC0705300)和天津市自然科学基金(批准号: 18JCQNJC05100)资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, Tianjin University, Tianjin 300072, China

2.
Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China

Corresponding author: Jiang Nan, nanj@tju.edu.cn ; Yang Shao-Qiong, shaoqiongy@tju.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11732010, 11572221, 11872272, U1633109, 11802195), the National Key R&D Program of China (Grant No. 2018YFC0705300), and the Natural Science Foundation of Tianjin, China (Grant No. 18JCQNJC05100).

文章全文

参考文献

[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

施引文献

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

Fig. 1. Schematic diagram of experimental plates: (a) Smooth plate; (b) riblets; (c) s-riblets

下载: 全尺寸图片幻灯片

图 2 正弦波沟槽截面图　(a) 左视图; (b) 俯视图

Fig. 2. Cross section of s-riblets: (a) Left view; (b) top view

下载: 全尺寸图片幻灯片

图 3 实验装置示意图　(a) case 1; (b) case 2

Fig. 3. Schematic diagram of experimental setup: (a) case 1; (b) case 2.

下载: 全尺寸图片幻灯片

图 4 不同壁面流场的流向平均速度剖面

Fig. 4. Mean velocity profiles in TBL flows over test plates

下载: 全尺寸图片幻灯片

图 5 不同壁面流场湍流度的分布曲线

Fig. 5. Distribution of turbulent intensities over test plates

下载: 全尺寸图片幻灯片

图 6 不同壁面流场雷诺切应力的分布曲线

Fig. 6. Distribution of Reynolds shear stress over test plates

下载: 全尺寸图片幻灯片

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

Fig. 7. Correlation coefficients of the streamwise fluctuation in $x-y$ plane over test plates

下载: 全尺寸图片幻灯片

图 8 特征向量空间中的局部流动^[50]

Fig. 8. The local motion in the space spanned by the eigenvectors^[50]

下载: 全尺寸图片幻灯片

图 9 $x-y$平面条件平均相干结构 (上) $y^{+}$ = 71.1; (下) $y^{+}$ = 128

Fig. 9. Conditionally-averaged structure in the $x-y$ plane: (top) $y^{+}$ = 71.1; (bottom) $y^{+}$ = 128

下载: 全尺寸图片幻灯片

图 10 Adrian等^[51]提出的发卡涡模型

Fig. 10. The model of hairpin vortex proposed by Adrian et al.^[51]

下载: 全尺寸图片幻灯片

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

Fig. 11. Instantaneous streamwise fluctuating velocity in $x-z$ plane at $y^{+}$ = 9.7

下载: 全尺寸图片幻灯片

图 12 不同壁面上流场$u'$沿展向的自相关函数

Fig. 12. Autocorrelation function of $u'$ in the $z$-direction over test plates

下载: 全尺寸图片幻灯片

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

下载: 导出CSV

map

[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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