二维有限长度柔性壁面上T-S波演化的数值研究

洪正; 叶正寅

doi:10.13700/j.bh.1001-5965.2021.0030

二维有限长度柔性壁面上T-S波演化的数值研究

doi: 10.13700/j.bh.1001-5965.2021.0030

洪正,
叶正寅^,

西北工业大学航空学院, 西安 710072

基金项目:

国家自然科学基金 12072281

详细信息

通讯作者:
叶正寅，E-mail: yezy@nwpu.edu.cn

中图分类号: V211.3
计量
- 文章访问数: 249
- HTML全文浏览量: 80
- PDF下载量: 186
- 被引次数: 0
出版历程
- 收稿日期: 2021-01-20
- 录用日期: 2021-03-07
- 网络出版日期: 2021-03-25
- 整期出版日期: 2022-07-20

Numerical investigation on evolution of T-S wave on a two-dimensional compliant wall with finite length

HONG Zheng,
YE Zhengyin^,

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Funds:

National Natural Science Foundation of China 12072281

More Information

Corresponding author: YE Zhengyin, E-mail: yezy@nwpu.edu.cn

摘要

摘要:
受自然界鸟类羽毛的柔性特征启发，利用数值模拟的方式开展了柔性壁面对亚声速边界层中T-S波演化的影响研究。刚性壁面上的数值结果与线性理论吻合得很好，验证了数值方法的可靠性。在此基础上，将部分刚性壁面替换为柔性壁面，结果表明，柔性壁面可以抑制T-S波在空间上的增长，从而推迟边界层流动转捩。壁面的变形不只跟随T-S波的波形，还因为柔性段与刚性段相接的前缘和后缘引起与扰动源频率相同的更大尺度的壁面波动，壁面的实际变形由这几种波叠加而成。开展的参数研究结果表明，增大表面的质量密度对于柔性壁面衰减扰动的效果几乎没有影响；增大表面张力和增加底部支撑的弹性系数可以增加壁面的刚性，减小壁面变形的幅度；增加阻尼可以抑制柔性段前后缘产生的大尺度壁面波动的传播，而对跟随T-S波的变形影响不大。总体上，柔性壁面的变形程度越大，其扰动的抑制效果越强。
- 柔性壁面 /
- 有限长度 /
- T-S波 /
- 边界层转捩 /
- 减阻
Abstract:
Inspired by the flexible characteristics of bird feathers, numerical simulations are used to study the influence of the compliant wall on the evolution of T-S wave in the subsonic boundary layer flow. First, the numerical results on the rigid wall are in good agreement with the linear stability theory, which verifies the reliability of the adopted numerical methods. On this basis, part of the rigid wall is replaced with a compliant wall, and the results show that the compliant wall can suppress the spatial growth of T-S wave, thus delaying the flow transition. Furthermore, the deformation of the compliant wall not only follows the waveform of T-S wave, but also includes larger-scale vibrations with the same frequency as the disturbance source, which are caused by the leading edge and trailing edge of the compliant section. The actual deformation of the compliant wall is a superposition of these waves. Later parameter study shows that increasing the surface mass density has almost no effect on the compliant wall in terms of attenuating disturbance. Increasing the surface tension or increasing the elastic coefficient of the foundation can increase the stiffness of the compliant wall and thus reduce the amplitude of wall deformation. Increasing the damping can suppress the propagation of large-scale wall vibrations generated at the leading edge and trailing edge of the compliant section, while having little effect on the deformation directly corresponding to T-S wave. The overall trend is that when the amplitude of wall deformation decreases, the attenuation effect of the compliant wall on T-S wave decreases.
- compliant wall /
- finite length /
- T-S wave /
- boundary-layer transition /
- drag reduction

HTML全文

图 1 计算域模型示意图

Figure 1. Schematic of computational domain

下载: 全尺寸图片幻灯片

图 2 y=0.65位置处的流向脉动速度沿空间的分布

Figure 2. Spatial distribution of streamwise velocity fluctuation along y=0.65

下载: 全尺寸图片幻灯片

图 3 本文计算与线性稳定性理论得到的中性点位置对比

Figure 3. Comparison of neutral points obtained from computations and linear stability theory

下载: 全尺寸图片幻灯片

图 4 不同网格下y=0.65位置处流向脉动速度沿空间的分布

Figure 4. Spatial distribution of streamwise velocity fluctuation along y=0.65 with different grids

下载: 全尺寸图片幻灯片

图 5 刚性壁面和柔性壁面条件下的流向脉动速度空间分布

Figure 5. Spatial distribution of streamwise velocity fluctuation with rigid wall and compliant wall

下载: 全尺寸图片幻灯片

图 6 柔性壁面和刚性壁面上y=0.65处流向脉动速度的空间分布

Figure 6. Spatial distribution of streamwise velocity fluctuation along y=0.65 on compliant wall and rigid wall

下载: 全尺寸图片幻灯片

图 7 不同时刻的壁面变形

Figure 7. Wall deformation at different times

下载: 全尺寸图片幻灯片

图 8 最终的壁面变形及其傅里叶变换结果

Figure 8. Final wall deformation and its Fourier transform results

下载: 全尺寸图片幻灯片

图 9 表面的质量密度对壁面变形的影响

Figure 9. Influence of surface mass density on wall deformation

下载: 全尺寸图片幻灯片

图 10 表面的质量密度对T-S波空间演化的影响

Figure 10. Influence of surface mass density on spatial evolution of T-S wave

下载: 全尺寸图片幻灯片

图 11 阻尼对壁面变形的影响

Figure 11. Influence of damping on wall deformation

下载: 全尺寸图片幻灯片

图 12 阻尼对T-S波空间演化的影响

Figure 12. Influence of damping on spatial evolution of T-S wave

下载: 全尺寸图片幻灯片

图 13 表面张力对壁面变形的影响

Figure 13. Influence of surface tension on wall deformation

下载: 全尺寸图片幻灯片

图 14 表面张力对T-S波空间演化的影响

Figure 14. Influence of surface tension on spatial evolution of T-S wave

下载: 全尺寸图片幻灯片

图 15 弹性系数对壁面变形的影响

Figure 15. Influence of elastic coefficient on wall deformation

下载: 全尺寸图片幻灯片

图 16 弹性系数对T-S波空间演化的影响

Figure 16. Influence of elastic coefficient on spatial evolution of T-S wave

下载: 全尺寸图片幻灯片

表 1 计算域流向参数

Table 1. Streamwise parameters of computational domain

参数	数值
x_in	55.85
x_r	135.08
x_cs	158.88
x_ce	777.10
x_out	900

下载: 导出CSV

表 2 不同柔性壁面的参数

Table 2. Parameters of different compliant walls

序号	m	d	T	k
1	1.45	0.1	14.5	0.069
2	7.25	0.1	14.5	0.069
3	1.45	0.5	14.5	0.069
4	1.45	0.1	29	0.069
5	1.45	0.1	14.5	0.69

下载: 导出CSV

参考文献(25)

[1]	屈秋林, 王晋军. 鸟类飞行空气动力学对人类飞行的启示[J]. 物理, 2016, 45(10): 640-644. doi: 10.7693/wl20161003 QU Q L, WANG J J. Human flight inspired by the aerodynamics of bird flight[J]. Physics, 2016, 45(10): 640-644(in Chinese). doi: 10.7693/wl20161003
[2]	VIDELER J J. Avian flight[M]. Oxford: Oxford University Press, 2006.
[3]	LINCOLN F C, PETERSON S R. Migration of birds[M]. [S. l. ]: US Fish and Wildlife Service, US Department of the Interior, 1979.
[4]	CROXALL J P, SILK J R, PHILLIPS R A, et al. Global circumnavigations: Tracking year-around ranges of nonbreeding albatrosses[J]. Science, 2005, 307(5707): 249-250. doi: 10.1126/science.1106042
[5]	GRAY J. Studies in animal locomotion VI-The propulsive powers of the dolphin[J]. Journal of Experimental Biology, 1936, 13(2): 192-199. doi: 10.1242/jeb.13.2.192
[6]	KRAMER M O. Boundary layer stabilization by distributed damping[J]. Journal of the Aerospace Sciences, 1960, 27(1): 69. doi: 10.2514/8.8380
[7]	KRAMER M O. Boundary layer stabilization by distributed damping[J]. Naval Engineers Journal, 1962, 74(2): 341-348. doi: 10.1111/j.1559-3584.1962.tb05568.x
[8]	GAD-EL-HAK M. Compliant coating for drag reduction[J]. Progress in Aerospace Sciences, 2002, 38(1): 77-99. doi: 10.1016/S0376-0421(01)00020-3
[9]	CARPENTER P W, GARRAD A D. The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 1. Tollmien-Schlichting instabilities[J]. Journal of Fluid Mechanics, 1985, 155: 465-510. doi: 10.1017/S0022112085001902
[10]	CARPENTER P W, GARRAD A D. The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instability[J]. Journal of Fluid Mechanics, 1986, 170: 199-232. doi: 10.1017/S002211208600085X
[11]	LEE C, KIM J. Control of the viscous sublayer for drag reduction[J]. Physics of Fluids, 2002, 14(7): 2523-2529. doi: 10.1063/1.1454997
[12]	DAVIES C, CARPENTER P W. Numerical simulation of the evolution of Tollmien-Schlichting waves over finite compliant panels[J]. Journal of Fluid Mechanics, 1997, 335: 361-392. doi: 10.1017/S0022112096004636
[13]	WANG Z, YEO K S, KHOO B C. On two-dimensional linear waves in Blasius boundary layer over viscoelastic layers[J]. European Journal of Mechanics-B/Fluids, 2006, 25(1): 33-58. doi: 10.1016/j.euromechflu.2005.04.006
[14]	DUNCAN J H. The response of an incompressible, viscoelastic coating to pressure fluctuations in a turbulent boundary layer[J]. Journal of Fluid Mechanics, 1986, 171: 339-363. doi: 10.1017/S0022112086001477
[15]	KIREIKO G V. Interaction of wall turbulence with a compliant surface[J]. Fluid Dynamics, 1990, 25(4): 550-554.
[16]	XU S, REMPFER D, LUMLEY J. Turbulence over a compliant surface: Numerical simulation and analysis[J]. Journal of Fluid Mechanics, 2003, 478: 11-34. doi: 10.1017/S0022112002003324
[17]	KIM E, CHOI H. Space-time characteristics of a compliant wall in a turbulent channel flow[J]. Journal of Fluid Mechanics, 2014, 756: 30-53. doi: 10.1017/jfm.2014.444
[18]	XIA Q J, HUANG W X, XU C X. Direct numerical simulation of turbulent boundary layer over a compliant wall[J]. Journal of Fluids and Structures, 2017, 71: 126-142. doi: 10.1016/j.jfluidstructs.2017.03.005
[19]	CHOI K S, YANG X, CLAYTON B R, et al. Turbulent drag reduction using compliant surfaces[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997, 453(1965): 2229-2240. doi: 10.1098/rspa.1997.0119
[20]	ZHANG C, WANG J, BLAKE W, et al. Deformation of a compliant wall in a turbulent channel flow[J]. Journal of Fluid Mechanics, 2017, 823: 345-390. doi: 10.1017/jfm.2017.299
[21]	JOZSA T I. Analytical solutions of incompressible laminar channel and pipe flow driven by in-plane wall oscillations[J]. Physics of Fluids, 2019, 31(8): 083605. doi: 10.1063/1.5104356
[22]	JOZSA T I, BALARAS E, KASHTALYAN M, et al. Active and passive in-plane wall fluctuations in turbulent channel flows[J]. Journal of Fluid Mechanics, 2019, 866: 689-720. doi: 10.1017/jfm.2019.145
[23]	LEE C, JIANG X. Flow structures in transitional and turbulent boundary layers[J]. Physics of Fluids, 2019, 31(11): 111301. doi: 10.1063/1.5121810
[24]	LIAO F, YE Z Y, ZHANG L X. Extending geometric conservation law to cell-centered finite difference method on stationary grids[J]. Journal of Computational Physics, 2015, 284: 419-433. doi: 10.1016/j.jcp.2014.12.040
[25]	FASEL H, KONZELMANN U. Nonparallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations[J]. Journal of Fluid Mechanics, 1990, 221: 311-347.