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本文采用基于纳米示踪平面激光散射技术的密度场测量方法，对Ma=3.0零压力梯度平板湍流边界层的密度场特性进行了实验研究，分析了边界层密度场的平均特性和脉动特性，并利用泰勒假设将空间信号转换为时域信号，对密度脉动的频谱特性进行了分析.研究发现，随着高度增加，边界层平均密度逐渐增大，但密度脉动仅在对数区内逐渐增大，在边界层外层却逐渐减小.密度脉动的概率密度函数在对数区内呈正态分布.从频谱特性可以发现，湍流边界层内部密度脉动具有丰富的脉动频率，最高达到MHz量级；在边界层近壁区和外层，密度脉动以低频分量为主；在对数区，高频分量与低频分量所占的比例基本相同.结合速度和密度同时测量发现，密度脉动与质量流量脉动在概率密度分布和频谱特性方面具有非常好的一致性，但与速度脉动相关性不大.超声速湍流边界层内部强烈密度脉动，及其与速度脉动的明显差别，是可压缩湍流边界层与不可压湍流边界层的显著区别之一.An experimental study on the density characteristics of a zero-pressure-gradient flat plate turbulent boundary layer at Ma=3.0 is performed by the density field measurement method based on Nano-tracer planar laser scattering (NPLS) technology. The mean and the fluctuating characteristics of the density field of the boundary layer are analyzed. And the spectrum analyses of density fluctuations are performed by utilizing Taylor's hypothesis to convert spatial measurements into pseudo-temporal measurements. The mean density profile increases away from the wall, which accords well with the density profile deduced from the mean velocity distribution by using the adiabatic Crocco-Busemann relation. The root mean square (RMS) of the density fluctuations increases in the logarithmic region with a peak value of 0.2ρ∞, and its probability density distribution follows a normal distribution. However, the RMS of density fluctuations decreases in the outer region of the boundary layer. According to the spectrum analysis, the density fluctuations are characterized in a wide range of frequencies throughout the boundary layer, with the maximum frequency on the order of 1 MHz. The low frequency fluctuations are predominant near the wall and in the outer region of the turbulent boundary layer. However, the proportion of high-frequency fluctuations is nearly equal to that of low-frequency fluctuations in the logarithmic region. The combined NPLS and PIV technique provide a simultaneous density and velocity measurements of the present turbulent boundary layer. The high frequency fluctuations in the supersonic turbulent boundary layer may be induced by the density fluctuations, which are caused by the convection of the turbulent structures with nonuniform density distributions. And the contribution of the velocity fluctuations only to the low frequency fluctuations is observed. There are good similarities between the density fluctuations and the mass flux fluctuations for both the probability density distribution and the spectrum characteristics. On the contrary, a large difference between the fluctuations of velocity and density is identified. Therefore, the strong density fluctuations inside supersonic turbulent boundary layers, as well as its difference between the velocity fluctuations, should be one of the most important differences between compressible and incompressible turbulent boundary layers.
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Keywords:
- supersonic /
- turbulent boundary layer /
- density field /
- spectrum analysis
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[2] Morkovin M V 1962 Int. Symp. on The Mechanics of Turbulence 367
[3] Smits A J, Dussauge J P 2006 Turbulent Shear Layers in Supersonic Flow (2nd Ed.) (New York:Springer) pp179-216
[4] Smits A J, Spina E F, Alving A E, Smith R W, Fernando E M, Donovan J F 1989 Phys. Fluids A 1 865
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[11] Mielke A F, Seasholtz R G, Elam K A, Panda J 2005 Exp. Fluids 39 441
[12] Mielke A F, Elam K A 2009 Exp. Fluids 47 673
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[15] Quan P C, Yi S H, Wu Y, Zhu Y Z, Chen Z 2013 Acta Phys. Sin. 62 084703 (in Chinese)[全鹏程, 易仕和, 武宇, 朱杨柱, 陈植2013物理学报62 084703]
[16] Wu Y, Yi S H, Chen Z, Zhang Q H, Gang D D 2013 Acta Phys. Sin. 62 184702 (in Chinese)[武宇, 易仕和, 陈植, 张庆虎, 冈敦殿2013物理学报62 184702]
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[21] He L, Yi S H, Tian L F, Chen Z, Zhu Y Z 2013 Chin. Phys. B 22 024704
[22] He L, Yi S H, Zhao Y X, Tian L F, Chen Z 2011 Sci. China:Ser. G 54 1702
[23] He L, Yi S H, Zhao Y X,Tian L F, Chen Z 2011 Chin. Sci. Bull. 56 489
[24] Zhao Y X, Yi S H, Tian L F, He L, Cheng Z Y 2010 Sci. China:Tech. Sci. 53 584
[25] Nau T 1995 M. S. Dissertation(Princeton:Princeton University)
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[1] Spina E F, Smits A J, Robinson S K 1994 Annu. Rev. Mech. 26 287
[2] Morkovin M V 1962 Int. Symp. on The Mechanics of Turbulence 367
[3] Smits A J, Dussauge J P 2006 Turbulent Shear Layers in Supersonic Flow (2nd Ed.) (New York:Springer) pp179-216
[4] Smits A J, Spina E F, Alving A E, Smith R W, Fernando E M, Donovan J F 1989 Phys. Fluids A 1 865
[5] Settles G S 2001 Schlieren & Shadowgraph Techniques (New York:Springer) pp263-278
[6] Tropea C, Yarin A, Foss J 2007 Handbook of Experimental Fluid Mechanics (New York:Springer) pp480-484
[7] Venkatakrishnan L 2004 AIAA 2004-2603
[8] Venkatakrishnan L, Meier G E A 2004 Exp. Fluids 37 237
[9] Danehy P M, O'Byrne S 1999 AIAA 1999-0772
[10] Martin J E, Garcia M H 2009 Exp. Fluids 46 265
[11] Mielke A F, Seasholtz R G, Elam K A, Panda J 2005 Exp. Fluids 39 441
[12] Mielke A F, Elam K A 2009 Exp. Fluids 47 673
[13] Tian L F, Yi S H, Zhao Y X, He L, Cheng Z Y 2009 Sci. China, Ser. G 52 1357
[14] He L 2006 M. S. Dissertation(Changsha:National University of Defense Technology) (in Chinese)[何霖2006硕士学位论文(长沙:国防科学技术大学)]
[15] Quan P C, Yi S H, Wu Y, Zhu Y Z, Chen Z 2013 Acta Phys. Sin. 62 084703 (in Chinese)[全鹏程, 易仕和, 武宇, 朱杨柱, 陈植2013物理学报62 084703]
[16] Wu Y, Yi S H, Chen Z, Zhang Q H, Gang D D 2013 Acta Phys. Sin. 62 184702 (in Chinese)[武宇, 易仕和, 陈植, 张庆虎, 冈敦殿2013物理学报62 184702]
[17] Zhu Y Z, Yi S H, Kong X P, Quan P C, Chen Z, Tian L F 2014 Acta Phys. Sin. 63 134701 (in Chinese)[朱杨柱, 易仕和, 孔小平, 全鹏程, 陈植, 田立丰2014物理学报63 134701]
[18] Liu X L 2015 M. S. Dissertation (Changsha:National University of Defense Technology) (in Chinese)[刘小林2015硕士学位论文(长沙:国防科学技术大学)]
[19] Zhao Y X, Yi S H, Tian L F, He L, Cheng Z Y 2010 Chin. Sci. Bull. 55 2004
[20] Chen Z, Yi S, He L, Zhu Y, Ge Y, Wu Y 2014 J. Visualization 17 345
[21] He L, Yi S H, Tian L F, Chen Z, Zhu Y Z 2013 Chin. Phys. B 22 024704
[22] He L, Yi S H, Zhao Y X, Tian L F, Chen Z 2011 Sci. China:Ser. G 54 1702
[23] He L, Yi S H, Zhao Y X,Tian L F, Chen Z 2011 Chin. Sci. Bull. 56 489
[24] Zhao Y X, Yi S H, Tian L F, He L, Cheng Z Y 2010 Sci. China:Tech. Sci. 53 584
[25] Nau T 1995 M. S. Dissertation(Princeton:Princeton University)
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