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摘要

以基于纳米示踪平面激光散射技术的密度场测量方法获得的 Ma= 3.0平板湍流边界层密度场实验数据为基础, 采用小波方法对湍流边界层密度脉动进行了多尺度与动态特性分析. 研究表明, 近壁区密度脉动概率密度呈偏离高斯分布, 大尺度分量对湍流边界层密度脉动起主导作用, 小尺度分量使概率密度呈“M”型分布; 采用希尔伯特变换对幅度调制效应进行分析, 结果表明超声速湍流边界层近壁处外层大尺度密度偏移会导致内层小尺度密度脉动的局部增强或减弱; 采用基于小波变换的时变谱密度估计对边界层不同高度的密度脉动进行分析, 结果表明脉动主要分布在1 MHz以内, 主导频段的密度脉动间歇性明显; 随着时间的发展, 大部分脉动存在频率从高频过渡到低频, 幅值先增加后减少的规律; 随着高度的增加, 对数区脉动主要分布在10 ⁵Hz以下, 尾迹区则集中在10 ⁵Hz以上, 边界层与主流交界处的脉动主要分布在两者相互作用形成的大尺度结构附近, 脉动能量从近壁面到主流区呈现先升高后降低的变化规律.

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Abstract

In order to obtain the time-varying information and dynamic characteristics of density fluctuation in compressible turbulence, the wavelet method is used to analyze the flow density field of zero-pressure-gradient flat plate turbulent boundary layer at Ma= 3.0, which is measured based on Nano-tracer plane laser scattering technique. Utilizing Taylor’s frozen hypothesis, the spatial signal of density field converts into the temporal signal. The one-dimensional orthogonal wavelet multi-resolution analysis is used to reveal multi-scale turbulent structures, and the results suggest that large-scale structures play a leading role in the density fluctuation of turbulent boundary layer while the small-scale structures make the probability density function (PDF) of density fluctuation manifested as an “M” distribution. The density fluctuation scalar PDF deviates from Gaussian distribution. The Hilbert transformation is used to analyze amplitude modulation effects between large- and small-scale structure, and the results suggest that positive (negative) large scale density excursion in the outer layer induces local enhancement (suppression) of the small scale density fluctuation in the inner layer near the wall. The time-varying spectral density estimation method based on the wavelet transform is used to analyze the density fluctuation at different heights of turbulent boundary layer after proving its viability in time and frequency domain. The results suggest a wide range of frequencies throughout the turbulent boundary layer, mainly distributed within 1 MHz. The density fluctuation in the dominant frequency band is intermittent, most of which transits from high frequency to low frequency while the spectral density first increases and then decreases. Near the wall, the time-frequency distributions of density fluctuation in the logarithmic layer are similar. In the middle part of the turbulent boundary layer, the frequency distribution and spectral density of the density fluctuation each reach a peak. Near the mainstream region, the spectral density decreases obviously, which is mainly distributed near the structure formed by the interaction between the boundary layer and mainstream. The wall constraint, viscous dissipation, and uniform mainstream make the fluctuation nearby the region relatively weak. As a result, the spectrum amplitude of density fluctuation first increases and then decreases from the wall to the mainstream.

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作者及机构信息

通信作者:何霖,helin_nudt@foxmail.com

基金项目:国家自然科学基金(批准号: 91752102)和长沙市杰出创新青年项目(批准号: KQ1802031)资助的课题

Authors and contacts

Corresponding author:He Lin,helin_nudt@foxmail.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 91752102) and the Excellent Innovation Young Project of Changsha, China (Grant No. KQ1802031)

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参考文献

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施引文献

下载: 全尺寸图片幻灯片

$M{a_\infty }$	${P_0}/{\rm MPa}$	${T_0}/{\rm K}$	${P_\infty }/{\rm Pa}$	${T_\infty }/{\rm K}$	${\rho _\infty }/{\rm kg \cdot {m^{ - 3} }}$	${U_\infty }/{\rm m \cdot {s^{ - 1} }}$	$\mu /{\rm Pa \cdot s}$	${R_e}/{\rm m^{ - 1} }$
3.0	0.1	300	2750	107	0.089	622.5	7.43 × 10^–6	7.49 × 10⁶

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