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Experimental study on the density characteristics of a supersonic turbulent boundary layer

He Lin Yi Shi-He Lu Xiao-Ge

Experimental study on the density characteristics of a supersonic turbulent boundary layer

He Lin, Yi Shi-He, Lu Xiao-Ge
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  • 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.
      Corresponding author: He Lin, helin@nudt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11302256).
    [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)

  • [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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  • Received Date:  18 July 2016
  • Accepted Date:  17 October 2016
  • Published Online:  20 January 2017

Experimental study on the density characteristics of a supersonic turbulent boundary layer

    Corresponding author: He Lin, helin@nudt.edu.cn
  • 1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11302256).

Abstract: 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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