三维空腔流动波系建模及模态演化

罗勇; 杨党国; 武从海; 李虎; 张树海; 吴军强

doi:10.7498/aps.71.20220922

摘要

高速空腔流动包含复杂波系结构, 这些复杂波系的传播和演化导致流动产生自持振荡而引起强噪声, 空腔噪声在频谱上包含多个具有离散频率的声模态, 深入理解各阶声模态的演化规律可为发展噪声控制方法提供理论基础. 通过分析亚声速和超声速情况下空腔两端的波系散射过程并考虑三维展向流动, 分别建立了针对亚声速和超声速空腔流动的三维波系模型. 三维波系模型包含了空腔中不同波系之间的非线性相互作用, 这种非线性作用可导致产生不同于Rossiter模态的其余频率成分. 基于三维空腔流动实验测量的压力信号数据, 对模型中的参数进行了线性估计, 采用快速傅里叶变换、双谱分析和小波变换等方法对压力信号进行了分析, 结果表明: 振荡主模态之间会产生非线性作用, 这种非线性作用产生了幅值较高的谐频, 主要的振荡模态之间存在模态切换现象, 且模态切换呈低频特征, 整体表现出随机性特性.

关键词:

Abstract

The high-speed flow passing through an open cavity will generate complex wave structures. The propagation and evolution of these waves can lead to the self-sustained oscillation of the cavity flow and cause strong noise. The cavity noise may contain multiple acoustic modes with discrete frequencies in the spectrum. A clear understanding of the evolution of the oscillation mode will provide a theoretical basis for the study of the noise control method. By analyzing the waves scattering process at both ends of the cavity at subsonic speed and supersonic speed and considering the three-dimensional spanwise flow, the three-dimensional wave model for subsonic cavity flow and supersonic cavity flow are established respectively. The model involves the nonlinear interaction between different waves in the cavity, which may produce other components different from the Rossiter mode. Based on the pressure signal data measured from the experiments on cavity flow for Mach numbers 0.9 and 1.5, the parameters in the model are linearly estimated. The pressure signals are analyzed by using FFT, bispectral analysis, and continuous wavelet transform. The results show that there are nonlinear interactions between the main oscillation modes, thus producing strong harmonics. The mode-switch phenomenon is observed in both the subsonic case and the supersonic case. The mode-switching exhibits low-frequency behavior and shows randomness as a whole.

Keywords:

作者及机构信息

1.
空气动力学国家重点实验室, 绵阳　621000

2.
中国空气动力研究与发展中心高速空气动力研究所, 绵阳　621000

通信作者: 李虎, lihu@cardc.cn

基金项目: 国家自然科学基金(批准号: 12102450, 12172374, 11732016)、四川省科技计划项目(批准号: 2018JZ0076)和国家数值风洞工程(NNW)资助的课题.

Authors and contacts

1.
1 State Key Laboratory of Aerodynamics, Mianyang 621000, China

2.
High Speed Aerodynamics Research Institute of Chinese Aerodynamics Research and Development Center, Mianyang 621000, China

Corresponding author: Li Hu, lihu@cardc.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12102450, 12172374, 11732016), the Science and Technology Program of Sichuan Province, China (Grant No. 2018JZ0076), and the National Numerical Windtunnel project, China.

文章全文 : translate this paragraph

参考文献

[1]	Dix R, Bauer R 2000 AIAA Paper 2000
[2]	Morton M 2007 AIAA Paper 2007
[3]	Gloerfelt X, Bogey C, Bailly C 2007 Cavity Noise (Paris: Arts et Métiers ParisTech)
[4]	Lawson S J, Barakos G N 2011 Prog. Aerosp. Sci 47 186 Google Scholar
[5]	郭启龙 2017 博士学位论文 (绵阳: 中国空气动力研究与发展中心研究生部) Guo Q L 2017 Ph. D. Dissertation (Mianyang: China Aerodynamics Research and Development Center Graduate School) (in Chinese)
[6]	Rossiter J E 1966 Aeron. Res. Counc. 3438
[7]	Powell A 1961 J. Acoust. Soc. Am 33 395 Google Scholar
[8]	Krishnamurty K 1956 Ph. D. Dissertation (Pasadena: California Institute of Technology)
[9]	Heller H H, Holmes D G, Covert E E 1971 J. Sound Vib 18 545 Google Scholar
[10]	Bilanin A J, Covert E E 1973 AIAA J 11 347 Google Scholar
[11]	Block P J W 1976 NASA Tech. Note D
[12]	Kerschen E, Tumin A 2003 AIAA Paper 2003
[13]	Alvarez J, Kerschen E, Tumin A 2004 AIAA Paper 2004
[14]	Ahuja K K, Mendoza J 1995 NASA C. R. 4653
[15]	Mendoza J, Ahuja K K 1995 AIAA Paper 95
[16]	Kegerise M A, Spina E F, Garg S, Cattafesta III L N 2004 Phys. Fluids 16 678 Google Scholar
[17]	Brès G A, Colonius T 2008 J. Fluid Mech 599 309 Google Scholar
[18]	Rowley C W, Colonius T, Basu A J 2002 J. Fluid Mech 455 315 Google Scholar
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[21]	韩帅斌, 罗勇, 张树海 2019航空工程进展 10 691 Han S B, Luo Y, Zhang S H 2019 Adv. Aero. Sci. Eng. 10 691 (in Chinese)
[22]	Cattafesta III L N, Garg S, Kegerise M, Jones G S 1998 AIAA Paper 98
[23]	Gloerfelt X, Bogey C, Bailly C 2003 Int. J. Aeroacoust 2 193 Google Scholar
[24]	Thangamani V 2019 AIAA J 57 1 Google Scholar
[25]	Luo Y, Wu C H, Yuan S Q, Tian H, Li H, Zhang S H 2021 32nd Congress of the International Council of the Aeronautical Sciences
[26]	Kegerise M A 1999 Ph. D. Dissertation University
[27]	Neary M D, Stephanoff K D 1987 Phys. Fluids 30 2936 Google Scholar
[28]	杨党国, 刘俊, 王显圣, 施傲, 周方奇, 郑晓东 2018 空气动力学学报 36 432 Yang D G, Liu J, Wang X S, Shi A, Zhou F Q, Zheng X D 2018 Acta Aerodyn. Sin. 36 432 (in Chinese)
[29]	Nikias C L, Raghuveer M R 1987 Proc. IEEE 75 869 Google Scholar
[30]	胡广书 2013 现代信号处理 (第二版) (北京: 清华大学出版社) Hu G S 2013 Modern Signal Processing (2nd Ed. ) (Beijing: Tsinghua University Press) (in Chinese)

施引文献

图 1 亚声速空腔中波系结构示意图

Fig. 1. Schematic diagram of wave structures of the subsonic cavity flow.

下载: 全尺寸图片幻灯片

图 2 超声速空腔中波系结构示意图

Fig. 2. Schematic diagram of wave structures of the supersonic cavity flow.

下载: 全尺寸图片幻灯片

图 3 三维空腔实验模型示意图(单位: mm)

Fig. 3. Schematic diagram of experimental cavity model (unit: mm).

下载: 全尺寸图片幻灯片

图 4 M = 1.5, 空腔底部压力信号总声压级两次重复性实验结果对比

Fig. 4. M = 1.5, comparison of two repeatable experiment results of OASPL of pressure signal at the bottom of cavity.

下载: 全尺寸图片幻灯片

图 5 空腔前壁测点压力信号声压级频谱(灰色竖线为(21)式预测值)　(a) M = 0.9; (b) M = 1.5

Fig. 5. The spectra of the pressure perturbation signals at the front wall of the cavity for two cases (the gray vertical line is the predicted frequencies by Eq. (21)): (a) M = 0.9; (b) M = 1.5.

下载: 全尺寸图片幻灯片

图 6 M = 1.5, 空腔前壁测点压力信号双谱分析相关系数　(a) 相关系数云图; (b) 局部放大

Fig. 6. M = 1.5, bicoherence spectrum of the pressure perturbation signals at the front wall of the cavity: (a) Contours of the correlation coefficient; (b) locally zoomed region of panel (a).

下载: 全尺寸图片幻灯片

图 7 两个马赫数的空腔前壁测点压力信号的连续小波变换结果　(a) M = 0.9 (注: 等值线范围(200, 3700)); (b) M = 1.5 (注: 等值线范围(300, 6000))

Fig. 7. The CWT results of the pressure perturbation signals at the front wall of the cavity for two Mach numbers: (a) M = 0.9 (contour levels between 200 to 3700); (b) M = 1.5 (contour levels between 300 to 6000).

下载: 全尺寸图片幻灯片

图 8 M = 0.9, 一阶、二阶模态小波变换系数随时间演化情况　(a) 一阶模态系数; (b) 二阶模态系数

Fig. 8. M = 0.9, the amplitude of the CWT coefficients of the dominant modes extracted from the CWT result: (a) Coefficient of the first mode; (b) Coefficient of the second mode.

下载: 全尺寸图片幻灯片

图 9 一阶、二阶模态小波变换系数的FFT频谱　(a) 一阶模态系数FFT; (b) 二阶模态系数FFT

Fig. 9. The FFT results of the CWT coefficients of the dominant modes in Fig. 8: (a) FFT of the coefficient of the first mode; (b) FFT of the coefficient of the second mode.

下载: 全尺寸图片幻灯片

图 10 一阶、二阶模态小波变换系数的PDF

Fig. 10. The probability density estimate of the CWT coefficients of the dominant modes in Fig. 8.

下载: 全尺寸图片幻灯片

表 1 不同马赫数下的实验参数

Table 1. The experimental parameters for different cases

Case Mach number Pressure/
Pa Temperature/K Reynold number(Re_L)

1 0.9 67938.3 247.85 3.41 × 10⁶
2 1.5 38080.2 198.62 4.28 × 10⁶

下载: 导出CSV

表 2 不同马赫数下的主导峰值频率

Table 2. The frequencies of the most energetic peaks for different cases.

Case f₁ f₂ f₃ f₄ f₅ f₆ f₇

1 330 940 1500 2112 2735 3344 3925
2 480 1264 2042 2871 3673 4468 —

下载: 导出CSV

[1]	Dix R, Bauer R 2000 AIAA Paper 2000
[2]	Morton M 2007 AIAA Paper 2007
[3]	Gloerfelt X, Bogey C, Bailly C 2007 Cavity Noise (Paris: Arts et Métiers ParisTech)
[4]	Lawson S J, Barakos G N 2011 Prog. Aerosp. Sci 47 186 Google Scholar
[5]	郭启龙 2017 博士学位论文 (绵阳: 中国空气动力研究与发展中心研究生部) Guo Q L 2017 Ph. D. Dissertation (Mianyang: China Aerodynamics Research and Development Center Graduate School) (in Chinese)
[6]	Rossiter J E 1966 Aeron. Res. Counc. 3438
[7]	Powell A 1961 J. Acoust. Soc. Am 33 395 Google Scholar
[8]	Krishnamurty K 1956 Ph. D. Dissertation (Pasadena: California Institute of Technology)
[9]	Heller H H, Holmes D G, Covert E E 1971 J. Sound Vib 18 545 Google Scholar
[10]	Bilanin A J, Covert E E 1973 AIAA J 11 347 Google Scholar
[11]	Block P J W 1976 NASA Tech. Note D
[12]	Kerschen E, Tumin A 2003 AIAA Paper 2003
[13]	Alvarez J, Kerschen E, Tumin A 2004 AIAA Paper 2004
[14]	Ahuja K K, Mendoza J 1995 NASA C. R. 4653
[15]	Mendoza J, Ahuja K K 1995 AIAA Paper 95
[16]	Kegerise M A, Spina E F, Garg S, Cattafesta III L N 2004 Phys. Fluids 16 678 Google Scholar
[17]	Brès G A, Colonius T 2008 J. Fluid Mech 599 309 Google Scholar
[18]	Rowley C W, Colonius T, Basu A J 2002 J. Fluid Mech 455 315 Google Scholar
[19]	Luo Y, Li H, Han S, Zhang S H 2021 Adv. Appl. Math. Mech 13 942 Google Scholar
[20]	韩帅斌, 罗勇, 李虎, 武从海, 张树海 2022 力学学报 54 359 Han S B, Luo Y, Li H, Wu C H, Zhang S H 2022 Chin. J. Theor. Appl. Mech. 54 359 (in Chinese)
[21]	韩帅斌, 罗勇, 张树海 2019航空工程进展 10 691 Han S B, Luo Y, Zhang S H 2019 Adv. Aero. Sci. Eng. 10 691 (in Chinese)
[22]	Cattafesta III L N, Garg S, Kegerise M, Jones G S 1998 AIAA Paper 98
[23]	Gloerfelt X, Bogey C, Bailly C 2003 Int. J. Aeroacoust 2 193 Google Scholar
[24]	Thangamani V 2019 AIAA J 57 1 Google Scholar
[25]	Luo Y, Wu C H, Yuan S Q, Tian H, Li H, Zhang S H 2021 32nd Congress of the International Council of the Aeronautical Sciences
[26]	Kegerise M A 1999 Ph. D. Dissertation University
[27]	Neary M D, Stephanoff K D 1987 Phys. Fluids 30 2936 Google Scholar
[28]	杨党国, 刘俊, 王显圣, 施傲, 周方奇, 郑晓东 2018 空气动力学学报 36 432 Yang D G, Liu J, Wang X S, Shi A, Zhou F Q, Zheng X D 2018 Acta Aerodyn. Sin. 36 432 (in Chinese)
[29]	Nikias C L, Raghuveer M R 1987 Proc. IEEE 75 869 Google Scholar
[30]	胡广书 2013 现代信号处理 (第二版) (北京: 清华大学出版社) Hu G S 2013 Modern Signal Processing (2nd Ed. ) (Beijing: Tsinghua University Press) (in Chinese)

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三维空腔流动波系建模及模态演化