余宇轩,等:正交圆柱尾迹的空间动力学行为的实验研究 377 SUZUKI,et al. Acoustic characteristics of two circular Ffk blinders forming a cross in uniform flow (effect on noise reduction and flow around both cylinders)p]. The Japan Society of Mechanical Engineers, 1987, 30(265) 附衰1Re=68下主导频率的空间演化(St=0.11) Table 1. The spatial evolution of the primary 1069-1079 frequencies at Re=68( St=0.11) 刀邓见,任安禄,邹建锋.垂直交叉双圆柱绕流数值模 拟及涡结构分析[空气动力学学报,2005,23(1) 热线位置圆柱间距L无量纲主导频率f 29-34 DENG Jian, REN An-lu, ZoU Jian-feng. Numerical 中心层 ld 4f/8 mulations of flow around two circular cylinder Acta Aerodynamica Sinica, 2005, 23(1): 29-34 8 WILLIAMSON C HK Vortex dynamics in the cylinder 中心层 ∫/8 wake]. Annual Review of Fluid Mechanics, 1996 剪切层 4f/8 6-20 [9 WILLIAMSON C H K. Three-dimensional wake transi- 剪切层 tion[J]. Journal of Fluid Mechanics, 1996, 328: 345- 2f/8,6f/8 [10胡海岩.应用非线性动力学[M北京,中国:航空工 剪切层 42-86 低频段 业出版社,2000 HU Hai-yan. Nonlinear dynamics[M]. Beijing, China 附衰2Re=84下主导频率的空间演化(Sr=0.13) Aviation Industry Press, 2000 Table 2. The spatial evolution of the primary [!]谢锡麟.开放流场空间动力学行为的一种实验研究 frequencies at Re=84( St=0.13) 框架及几类经典流场研究[D].博士论文,复旦大学, 热线圆柱无量纲 位置间距L尺度x/d 主导频率f 上海,中国,2004 XIE XI-Iin. The framework of an experimental study of中心层1d 6-86 4f/8 the dynamic behavior of open flow field space and a 6f/8 few classic flow field Doctoral Thesis, Fudan Uni- 1尚宣廷,谢锡麟,麻伟巍,等基于自谱及互谱实验中心层M19262f/8,f/8,12/ versity, Shanghai, China, 2004 f/8 研究二维单圆柱尾迹空间动力学行为力学季刊 53-86 2010,31(3):319-328. 2f/8,f/8 SHANG Xuan-ting, XIE Xi-lin, MAR Wei-wei, et al. ∫/8 中心层 14-42 of two dimensional wakes of a circular-cylinder based 42-86 2f/8,f/8 on self- and cross-spectra[]. Chinese Quarterly of Me chanics,2010,31(3)319-328 剪切层1d 4f/8 []]谢锡麟,麻伟巍.真实开放流场空间动力学行为分析 6-175 的基本思想及方法[中国科技论文在线精品论文 剪切层 17.5-40 6f/8 2012,5(3):250-259 IE Xi-lin, MA Wei-wei. The primary ideas and metho- f/8 logies of spatial dyr amIcs 6-38 and some contemporary developments]. Onlin 剪切层6d 38-86 低频段 shedinhttp://www.paperedu.cn/,2012,5(3):250-259余宇轩，等：正交圆柱尾迹的空间动力学行为的实验研究 377 SUZUKI, et al. Acoustic characteristics of two circular cylinders forming a cross in uniform flow (effect on noise reduction and flow around both cylinders)[J]. The Japan Society of Mechanical Engineers, 1987, 30(265): 1069-1079. [7] 邓见, 任安禄, 邹建锋. 垂直交叉双圆柱绕流数值模 拟及涡结构分析[J]. 空气动力学学报, 2005, 23(1): 29-34. DENG Jian, REN An-lu, ZOU Jian-feng. Numerical simulations of flow around two circular cylinders in cruciform arrangement and vortex structures analysis[J]. Acta Aerodynamica Sinica, 2005, 23(1): 29-34. [8] WILLIAMSON C H K. Vortex dynamics in the cylinder wake[J]. Annual Review of Fluid Mechanics, 1996, 28: 477-539. [9] WILLIAMSON C H K. Three-dimensional wake transi￾tion[J]. Journal of Fluid Mechanics, 1996, 328: 345- 407. [10] 胡海岩. 应用非线性动力学[M]. 北京, 中国: 航空工 业出版社, 2000. HU Hai-yan. Nonlinear dynamics[M]. Beijing, China: Aviation Industry Press, 2000. [11] 谢锡麟. 开放流场空间动力学行为的一种实验研究 框架及几类经典流场研究[D]. 博士论文, 复旦大学, 上海, 中国, 2004. XIE Xi-lin. The framework of an experimental study of the dynamic behavior of open flow field space and a few classic flow field[D]. Doctoral Thesis, Fudan Uni￾versity, Shanghai, China, 2004. [12] 尚宣廷, 谢锡麟, 麻伟巍, 等. 基于自谱及互谱实验 研究二维单圆柱尾迹空间动力学行为[J]. 力学季刊, 2010, 31(3): 319-328. SHANG Xuan-ting, XIE Xi-lin , MAR Wei-wei, et al. Experimental studies on the spatial dynamical behaviors of two dimensional wakes of a circular-cylinder based on self- and cross-spectra[J]. Chinese Quarterly of Me￾chanics, 2010, 31(3): 319-328. [13] 谢锡麟, 麻伟巍. 真实开放流场空间动力学行为分析 的基本思想及方法[J]. 中国科技论文在线精品论文, 2012, 5(3): 250-259. XIE Xi-lin, MA Wei-wei. The primary ideas and metho￾logies of spatial dynamics analysis of real open flows and some contemporary developments[J]. Online publi￾shed in http://www.paper.edu.cn/, 2012, 5(3): 250-259. 附录: 附表 1 Re = 68 下主导频率的空间演化（ St = 0.11） Table 1. The spatial evolution of the primary frequencies at Re = 68 ( St = 0.11) 热线位置 圆柱间距 L 无量纲 尺度 x / d 主导频率 z f 中心层 1d 6-86 4 /8 f 中心层 3d 6-20 6 /8 f 20-86 2 /8 f , f / 8 中心层 6d 6-86 f /8 剪切层 1d 6-86 4 /8 f 剪切层 3d 6-20 f 20-86 2 /8 f , 6 /8 f 剪切层 6d 6-42 f 42-86 低频段 附表 2 Re = 84 下主导频率的空间演化（ St = 0.13） Table 2. The spatial evolution of the primary frequencies at Re = 84 ( St = 0.13) 热线 位置 圆柱 间距 L 无量纲 尺度 x / d 主导频率 z f 中心层 1d 6-86 4 /8 f 中心层 3d 6-19 6 /8 f 19-26 2 /8 f , f / 8 , 12 /8 f 26-53 f / 8 53-86 2 /8 f , f / 8 中心层 6d 6-14 f / 8 14-42 7 /8 f 42-86 2 /8 f , f / 8 剪切层 1d 6-86 4 /8 f 剪切层 3d 6-17.5 f 17.5-40 6 /8 f 40-86 f / 8 剪切层 6d 6-38 f 38-86 低频段