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Mixing enhancement for supersonic mixing layer by using plasma synthetic jet

Wang Peng Shen Chi-Bing

Mixing enhancement for supersonic mixing layer by using plasma synthetic jet

Wang Peng, Shen Chi-Bing
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  • Mixing enhancement for supersonic mixing layer is of great importance for developing scramjet engine. The growth rate of supersonic mixing layer is smaller than that of subsonic mixing layer. As the compressibility increases, the mixing enhancement becomes more difficult. Plasma synthetic jet is regarded as a promising flow control technology. The plasma synthetic jet generator can produce high energy jet. This generator has no moving parts and does not need additional gas source. It is the first time that plasma synthetic jet has been used to enhance the mixing in supersonic mixing layers. The influence of plasma synthetic jet on the supersonic mixing layer is investigated experimentally and numerically. The experiments are conducted in the low noise supersonic mixing layer wind tunnel. The Mach number of upper stream and lower stream are 1.37 and 2.39 respectively. The convective Mach number of this wind tunnel is 0.32. The plasma synthetic jet actuators are installed in the splitter plate. The distance between the jet hole and the splitter plate end is 15 mm. The nanoparticle-based planar laser scattering (NPLS), particle image velocimetry (PIV) and schlieren are used to obtain the response of the supersonic mixing layer to single pulse plasma synthetic jet perturbation. The NPLS successfully captures the large-scaled vortex structures induced by the plasma synthetic jet in the supersonic mixing layers. The effect of plasma synthetic jet is remarkable. The schlieren images show the process of the perturbation. An oblique shock wave is generated when the jet is ejected. The PIV is employed to obtain the influence of plasma synthetic jet on the velocity field. The y-velocity standard deviation increases due to the perturbation. The actuators’ mixing enhancement effects and actuators’ performances at three locations are investigated by two-dimensional numerical simulation. The three actuators are located on the upper, bottom and end surface of splitter plate respectively. The numerical simulation results show that the mixing layer thickness is increased by the plasma synthetic jet perturbation. There are two mechanisms of perturbations while actuators are located at different positions. The actuators installed on the upper and bottom surface of splitter plate influence the mixing layer through perturbing the upper and lower stream respectively. The actuator installed at the end of splitter plate affects the mixing layer directly. The response time of supersonic mixing layers to the perturbation of the actuator installed at the end of splitter plate is shorter than those of the others. The performance of each actuator is sensitive to the location.
      Corresponding author: Shen Chi-Bing, cbshen@nudt.edu.cn
    [1]

    Zang A, Tempel T, Yu K, Buckley S 2005 43rd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, 10−13 January, 2005 p1423

    [2]

    Gutmark E J, Schadow C S, Yu K H 1995 Annu. Rev. Fluid Mech. 27 375

    [3]

    Zhang C X, Liu Y, Fu B S, Yu X J 2018 Acta Astronaut. 153 50

    [4]

    Haimovitch Y, Gartenberg E, Roberts J A, Northam G 1994 30th Joint Propulsion Conference and Exhibit Indianapolis, IN, 27−29 June, 1994 p2940

    [5]

    Guirguis R, Grinstein F, Young T, Oran E, Kailasanath K 1987 25th AIAA Aerospace Sciences Meeting Reno, Nevada, 12−15 January, 1987 p0373

    [6]

    Seiner J M, Dash S M, Kenzakowski D C 2001 J. Propul. Power 17 1273

    [7]

    Collin E, Barre S, Bonnet J P 2004 Phys. Fluids 16 765

    [8]

    Fernando E M, Menon S 1993 AIAA J. 31 278

    [9]

    Kharitonov A, Lokotko A, Tchernyshyev A, Kopchenov V, Lomkov K, Rudakov A 2000 38th Aerospace Sciences Meeting and Exhibit Reno, Nevada, 10−13 January, 2000 p0559

    [10]

    Freeman A P, Catrakis H J 2009 J. Turbul. 10 1

    [11]

    Adelgren R G, Elliott G S, Crawford J B, Carter C D, Donbar J M, Grosjean D F 2005 AIAA J. 43 776

    [12]

    Zhang D, Tan J, Liang L 2015 Acta Astronaut. 117 440

    [13]

    Narayanaswamy V, Shin J, Clemens N, Raja L 2008 46th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 7−10, 2008 p285

    [14]

    Grossman K, Bohdan C, van Wie D 2003 41st Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 6−9 , 2003 p57

    [15]

    Grossman K, Cybyk B, van Wie D, Rigling M 2004 42nd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 5−8 , 2004 p89

    [16]

    王林, 夏智勋, 罗振兵, 周岩, 张宇 2014 物理学报 63 194702

    Wang L, Xia Z X, Luo Z B, Zhou Y, Zhang Y 2014 Acta Phys. Sin. 63 194702

    [17]

    Narayanaswamy V, Raja L L, Clemens N T 2012 Phys. Fluids 24 076101

    [18]

    Zhou Y, Xia Z X, Luo Z B, Wang L 2016 Sci. China Technol. Sc. 60 146

    [19]

    王宏宇, 李军, 金迪, 代辉, 甘甜, 吴云 2017 物理学报 66 084705

    Wang H Y, Li J, Jin D, Dai H, Can T, Wu Y 2017 Acta Phys. Sin. 66 084705

    [20]

    Hardy P, Barricau P, Caruana D, Gleyzes C, Belinger A, Cambronne J P 2010 40th Fluid Dynamics Conference and Exhibit Chicago, Illinois, 28 June−1 July, 2010 p5103

    [21]

    Huet M 2014 20th AIAA/CEAS Aeroacoustics Conference Atlanta, GA, June 16−20 , 2014 p2620

    [22]

    Chedevergne F, Léon O, Bodoc V, Caruana D 2015 Int. J. Heat Fluid Fl. 56 1

    [23]

    Bogdanoff D W 1983 AIAA J. 21 926

    [24]

    Papamoschou D 1991 AIAA J. 29 680

    [25]

    Arvind S, Jamey D J 2007 J. Phys. D: Appl. Phys. 40 637

    [26]

    Zhou Y, Xia Z X, Luo Z B, Wang L, Deng X 2017 Acta Astronaut. 133 95

    [27]

    Haack S, Taylor T, Z. Cybyk B, H. Foster C, Alvi F 2011 42nd AIAA Plasmadynamics and Lasers Conference Honolulu, Hawaii, 27−30 June, 2011 p3997

    [28]

    赵玉新 2008 博士学位论文(长沙: 国防科技大学)

    Zhao Y X 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

    [29]

    罗振兵 2006 博士学位论文(长沙: 国防科技大学)

    Luo Z B 2006 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

    [30]

    Narayanaswamy V, Raja L L, Clemens N T 2010 AIAA J. 48 297

    [31]

    Freeman L J 2014 Master Thesis (California Polytechnic State University)

    [32]

    周岩 2018 博士学位论文 (长沙: 国防科技大学)

    Zhou Y 2018 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

  • 图 1  超声速混合层风洞示意图

    Figure 1.  Schematic of the supersonic mixing layer wind tunnel.

    图 2  超声速混合层风洞实物图

    Figure 2.  The test section of supersonic mixing layer wind tunnel.

    图 3  安装有等离子体合成射流激励器隔板在风洞中的位置 (a) 隔板在风洞中位置; (b) 激励器在隔板上的位置

    Figure 3.  Schematic of the wind tunnel and the actuator mounted inside a plate: (a) Splitter plate in the wind tunnel; (b) actuator in the splitter plate.

    图 4  两电极等离子体合成射流激励器

    Figure 4.  Two-electrode plasma synthetic actuator

    图 5  纹影系统示意图

    Figure 5.  The schematic diagram of schlieren system

    图 6  等离子体合成射流试验系统的时序示意图

    Figure 6.  Schematics of the experimental system sequence chart.

    图 7  纹影结果 (a) T0 + 0 μs; (b) T0 + 67 μs; (c) T0 + 233 μs

    Figure 7.  Schlieren images: (a) T0 + 0 μs; (b) T0 + 67 μs; (c) T0 + 233 μs.

    图 8  等离子体合成射流对超声速混层作用的NPLS结果 (a) 未受扰动; (b) T0 + 180 μs; (c) T0 + 230 μs

    Figure 8.  NPLS images of supersonic mixing layer under perturbation and unperturbation: (a) Unperturbation; (b) T0 + 180 μs; (c) T0 + 230 μs.

    图 9  PIV的实验结果 (a) 流向速度的平均结果; (b) T0 + 230 μs时刻流向速度的平均结果; (c) 横向速度标准差; (d) T0 + 230 μs时刻横向速度标准差

    Figure 9.  PIV experimental results: (a) Averaged X-velocity; (b) averaged X-velocity at T0 + 230 μs; (c) Y-velocity standard deviation; (d) Y-velocity standard deviation at T0 + 230 μs.

    图 10  仿真物理模型 (a) 无扰动; (b) 激励器在隔板上表面; (c) 激励器在隔板尾端; (d) 激励器在隔板下表面

    Figure 10.  Physical model: (a) Unperturbation; (b) the actuator at the upper surface of the splitter plate; (c) the actuator at the end surface of splitter plate; (d) the actuator at bottom surface of splitter plate.

    图 11  算例验证的计算模型及网格

    Figure 11.  Calculation model and grid for code validation.

    图 12  网格无关性及算例验证

    Figure 12.  Certification of grid independence and code validation

    图 13  (T0 + 67 μs)时刻纹影实验结果与数值纹影结果对比 (a) 纹影实验结果; (b) 数值纹影结果

    Figure 13.  T0 + 67 μs, numerical and experimental schlierens: (a) Experimental schlieren; (b) numerical schlieren.

    图 14  (T0 + 180 μs)时刻NPLS结果与数值仿真密度场对比 (a) NPLS结果; (b) 数值仿真密度场

    Figure 14.  T0 + 180 μs, contour of density and NPLS result: (a) NPLS result; (b) contour of density.

    图 15  (T0 + 555 μs)时刻密度场 (a) 未受扰动; (b) 激励器在隔板上表面; (c) 激励器在隔板尾端; (d) 激励器在隔板下表面

    Figure 15.  Contours of density at T0 + 555 μs: (a) Unperturbation; (b) the actuator at the upper surface of the splitter plate; (c) the actuator at the end surface of the splitter plate; (d) the actuator at the bottom surface of the splitter plate.

    图 16  (T0 + 75 μs)时刻温度云图和流线 (a) 激励器在隔板上表面; (b) 激励器在隔板尾端

    Figure 16.  Simulation of the temperature and flow: (a) The actuator at the upper surface of the splitter plate; (b) the actuator at the end surface of the splitter plate

    图 17  时均速度混合层厚度

    Figure 17.  Time-averaged velocity thickness of mixing layer

    图 18  激励器出口参数 (a) 激励器出口质量流量; (b) 激励器出口速度; (c) 激励器出口动量率; (d) 激励器出口压力

    Figure 18.  The parameters of actuator outlet: (a) The mass flow rate of actuator outlet; (b) the velocity of actuator outlet; (c) the momentum rate of actuator outlet; (d) the pressure of actuator outlet.

    图 19  激励器腔体内参数 (a) 激励器腔体密度; (b) 激励器腔体内温度; (c) 激励器腔体内压力

    Figure 19.  Parameters of actuator cavity: (a) Density of the gas in the actuator chamber; (b) temperature of the gas in the actuator chamber; (c) pressure of the gas in the actuator chamber.

    表 1  压力匹配情况下校测流场参数

    Table 1.  Flow parameters of supersonic mixing layer.

    马赫数Ma速度U/m·s–1静温T/K总温T0/K运动黏度μ/
    10–5 m2·s–1
    1.37405.16218.393001.4312
    2.39567.18139.873000.9635
    DownLoad: CSV
  • [1]

    Zang A, Tempel T, Yu K, Buckley S 2005 43rd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, 10−13 January, 2005 p1423

    [2]

    Gutmark E J, Schadow C S, Yu K H 1995 Annu. Rev. Fluid Mech. 27 375

    [3]

    Zhang C X, Liu Y, Fu B S, Yu X J 2018 Acta Astronaut. 153 50

    [4]

    Haimovitch Y, Gartenberg E, Roberts J A, Northam G 1994 30th Joint Propulsion Conference and Exhibit Indianapolis, IN, 27−29 June, 1994 p2940

    [5]

    Guirguis R, Grinstein F, Young T, Oran E, Kailasanath K 1987 25th AIAA Aerospace Sciences Meeting Reno, Nevada, 12−15 January, 1987 p0373

    [6]

    Seiner J M, Dash S M, Kenzakowski D C 2001 J. Propul. Power 17 1273

    [7]

    Collin E, Barre S, Bonnet J P 2004 Phys. Fluids 16 765

    [8]

    Fernando E M, Menon S 1993 AIAA J. 31 278

    [9]

    Kharitonov A, Lokotko A, Tchernyshyev A, Kopchenov V, Lomkov K, Rudakov A 2000 38th Aerospace Sciences Meeting and Exhibit Reno, Nevada, 10−13 January, 2000 p0559

    [10]

    Freeman A P, Catrakis H J 2009 J. Turbul. 10 1

    [11]

    Adelgren R G, Elliott G S, Crawford J B, Carter C D, Donbar J M, Grosjean D F 2005 AIAA J. 43 776

    [12]

    Zhang D, Tan J, Liang L 2015 Acta Astronaut. 117 440

    [13]

    Narayanaswamy V, Shin J, Clemens N, Raja L 2008 46th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 7−10, 2008 p285

    [14]

    Grossman K, Bohdan C, van Wie D 2003 41st Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 6−9 , 2003 p57

    [15]

    Grossman K, Cybyk B, van Wie D, Rigling M 2004 42nd AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 5−8 , 2004 p89

    [16]

    王林, 夏智勋, 罗振兵, 周岩, 张宇 2014 物理学报 63 194702

    Wang L, Xia Z X, Luo Z B, Zhou Y, Zhang Y 2014 Acta Phys. Sin. 63 194702

    [17]

    Narayanaswamy V, Raja L L, Clemens N T 2012 Phys. Fluids 24 076101

    [18]

    Zhou Y, Xia Z X, Luo Z B, Wang L 2016 Sci. China Technol. Sc. 60 146

    [19]

    王宏宇, 李军, 金迪, 代辉, 甘甜, 吴云 2017 物理学报 66 084705

    Wang H Y, Li J, Jin D, Dai H, Can T, Wu Y 2017 Acta Phys. Sin. 66 084705

    [20]

    Hardy P, Barricau P, Caruana D, Gleyzes C, Belinger A, Cambronne J P 2010 40th Fluid Dynamics Conference and Exhibit Chicago, Illinois, 28 June−1 July, 2010 p5103

    [21]

    Huet M 2014 20th AIAA/CEAS Aeroacoustics Conference Atlanta, GA, June 16−20 , 2014 p2620

    [22]

    Chedevergne F, Léon O, Bodoc V, Caruana D 2015 Int. J. Heat Fluid Fl. 56 1

    [23]

    Bogdanoff D W 1983 AIAA J. 21 926

    [24]

    Papamoschou D 1991 AIAA J. 29 680

    [25]

    Arvind S, Jamey D J 2007 J. Phys. D: Appl. Phys. 40 637

    [26]

    Zhou Y, Xia Z X, Luo Z B, Wang L, Deng X 2017 Acta Astronaut. 133 95

    [27]

    Haack S, Taylor T, Z. Cybyk B, H. Foster C, Alvi F 2011 42nd AIAA Plasmadynamics and Lasers Conference Honolulu, Hawaii, 27−30 June, 2011 p3997

    [28]

    赵玉新 2008 博士学位论文(长沙: 国防科技大学)

    Zhao Y X 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

    [29]

    罗振兵 2006 博士学位论文(长沙: 国防科技大学)

    Luo Z B 2006 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

    [30]

    Narayanaswamy V, Raja L L, Clemens N T 2010 AIAA J. 48 297

    [31]

    Freeman L J 2014 Master Thesis (California Polytechnic State University)

    [32]

    周岩 2018 博士学位论文 (长沙: 国防科技大学)

    Zhou Y 2018 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

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Publishing process
  • Received Date:  06 May 2019
  • Accepted Date:  09 June 2019
  • Available Online:  26 November 2019
  • Published Online:  01 September 2019

Mixing enhancement for supersonic mixing layer by using plasma synthetic jet

    Corresponding author: Shen Chi-Bing, cbshen@nudt.edu.cn
  • Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

Abstract: Mixing enhancement for supersonic mixing layer is of great importance for developing scramjet engine. The growth rate of supersonic mixing layer is smaller than that of subsonic mixing layer. As the compressibility increases, the mixing enhancement becomes more difficult. Plasma synthetic jet is regarded as a promising flow control technology. The plasma synthetic jet generator can produce high energy jet. This generator has no moving parts and does not need additional gas source. It is the first time that plasma synthetic jet has been used to enhance the mixing in supersonic mixing layers. The influence of plasma synthetic jet on the supersonic mixing layer is investigated experimentally and numerically. The experiments are conducted in the low noise supersonic mixing layer wind tunnel. The Mach number of upper stream and lower stream are 1.37 and 2.39 respectively. The convective Mach number of this wind tunnel is 0.32. The plasma synthetic jet actuators are installed in the splitter plate. The distance between the jet hole and the splitter plate end is 15 mm. The nanoparticle-based planar laser scattering (NPLS), particle image velocimetry (PIV) and schlieren are used to obtain the response of the supersonic mixing layer to single pulse plasma synthetic jet perturbation. The NPLS successfully captures the large-scaled vortex structures induced by the plasma synthetic jet in the supersonic mixing layers. The effect of plasma synthetic jet is remarkable. The schlieren images show the process of the perturbation. An oblique shock wave is generated when the jet is ejected. The PIV is employed to obtain the influence of plasma synthetic jet on the velocity field. The y-velocity standard deviation increases due to the perturbation. The actuators’ mixing enhancement effects and actuators’ performances at three locations are investigated by two-dimensional numerical simulation. The three actuators are located on the upper, bottom and end surface of splitter plate respectively. The numerical simulation results show that the mixing layer thickness is increased by the plasma synthetic jet perturbation. There are two mechanisms of perturbations while actuators are located at different positions. The actuators installed on the upper and bottom surface of splitter plate influence the mixing layer through perturbing the upper and lower stream respectively. The actuator installed at the end of splitter plate affects the mixing layer directly. The response time of supersonic mixing layers to the perturbation of the actuator installed at the end of splitter plate is shorter than those of the others. The performance of each actuator is sensitive to the location.

    • 随着高超声速飞行器的发展, 作为实现方式之一的超燃冲压发动机成为研究热点. 在超燃冲压发动机中, 燃料和氧化剂的快速掺混可以减小燃烧室的长度, 提高燃烧效率[1-3]. 由于燃料和空气在燃烧室内停留时间为微秒量级[4], 如何快速地实现燃料和氧化剂的混合, 是发展超燃冲压发动机的关键技术之一. 以此为背景的超声速混合层增强混合成为一个研究的热点. 相对于亚声速混合层, 超声速混合层厚度的空间增长率较低[5], 随着压缩性增强的混合难度越来越大[2]. 寻找超声速混合层增强混合的方法具有十分重要的实际意义.

      增强混合的装置一般是基于加快失稳、加快诱导涡结构原理设计的. 混合增强的方式可以分为主动增强和被动增强[6]. 被动增强是改变尾缘结构, 常见的被动混合增强构型有波瓣、锯齿等[7-9]. 主动增强是向流场周期性的注入能量, 常见的方式有机械振动、射流扰动和放电激励[10-12]. 被动增强混合虽然具有简单易行的特点, 但是不能根据情况改变. 较被动增强混合方式而言, 主动增强混合方式可以弥补这一缺陷, 并且能在增强混合的同时降低总压损失. 虽然主动增强混合是较为有效的增强混合方式, 但传统的主动增强混合手段仍存在能量较低、响应慢、需要附加气源等方面的不足.

      等离子体合成射流是一种新的控制手段, 具有能量密度高、响应速度快、无需额外的气源和没有机械活动部件的优势, 弥补传统主动增强混合的不足[13-15]. 此外等离子合成射流的扰动还具有一定的方向性. 等离子体合成射流工作原理可以简单表述为: 在激励器腔内放电将气体加热, 腔体内气体受热后压力上升, 气体从小孔喷出对外膨胀做功. 等离子体合成射流不同于直接暴露在流场中的放电激励. 等离子体合成射流是通过产生的射流和压缩波对流场进行扰动. 直接暴露在流场中的放电激励是通过快速局部焦耳热效应产生的压缩波和电流体动力学效应对流场实现扰动[16].

      以等离子体合成射流作为控制手段, 在超声速流动中主要应用于边界层和激波的控制[17-19], 对于混合层的控制主要还停留在亚声速. Hardy等[20]实验研究了等离子合成射流对亚声速射流的控制, 实验结果表明等离子体合成射流诱导出涡结构使射流剪切层变厚. Huet[21]采用数值仿真方法研究了等离子体合成射流对亚声速射流的流动控制, 实现了降低噪音. Chedevergne等[22]采用实验加数值仿真的方法研究了等离子体合成射流对马赫数为0.6的高雷诺数射流的流动控制机理. 作为一种对混合层的控制手段, 等离子体合成射流在亚声速中表现出较强的控制能力.

      等离子体合成射流用于超声速混合层的控制目前研究的较少. 本文将采用实验加仿真的方法, 验证等离子合成射流对超声速混合层控制的有效性, 分析对比激励器布置位置不同对激励器性能以及混合增强效果的影响, 为在超声速流场中设计高效的增强混合方案提供参考.

    2.   实验设备
    • 实验在低噪声超声速混合层风洞中进行. 混合层风洞如图1所示, 实验段长度为350 mm, 高度为60 mm, 宽度为200 mm. 为消除流向压力梯度, 风洞的上下壁面有1°的张角. 厚度为10 mm的隔板从风洞入口到喷管出口将风洞从中间分为两部分. 风洞实验段实物图如图2所示. 风洞上侧喷管马赫数为1.37, 风洞下侧喷管马赫数为2.39, 根据对流马赫数(Mc)计算公式[23,24]

      Figure 1.  Schematic of the supersonic mixing layer wind tunnel.

      Figure 2.  The test section of supersonic mixing layer wind tunnel.

      其中U1是上侧气流流向速度, U2为下侧气流流向速度, a1为上侧气流声速, a2为下侧气流声速. 所得对流马赫数为0.3, 具体参数见表1. 上侧气流的总压调节器用于在实验段实现静压匹配.

      马赫数Ma速度U/m·s–1静温T/K总温T0/K运动黏度μ/
      10–5 m2·s–1
      1.37405.16218.393001.4312
      2.39567.18139.873000.9635

      Table 1.  Flow parameters of supersonic mixing layer.

    • 等离子体合成射流的详细原理在文献[25-27]中有较多的介绍. 图3是安装有等离子体激励器阵列隔板的示意图. X, Y, Z分别代表流向、横向和展向的方向. 激励器安装在距离隔板尾端约15 mm处, 实现对上侧气流的扰动. 5个激励器采用串联放电方式工作. 每个激励器由圆柱形放电腔体和一对电极组成. 采用抗放电烧蚀能力强的钨针作为电极, 电极直径为1 mm, 腔体采用的是树脂材料. 放电电极之间的间距为1 mm. 圆柱形放电腔体的直径为12 mm、高度为6 mm、体积为678.24 mm3. 有一个直径为2.5 mm的射流孔, 如图4所示. 电源采用KD-1高压脉冲电源[16], 最大输出电压为10 kV, 脉冲频率为1—50 Hz, 单次脉冲最大输出能量为20 J. 本次实验使用的放电电容为640 nF.

      Figure 3.  Schematic of the wind tunnel and the actuator mounted inside a plate: (a) Splitter plate in the wind tunnel; (b) actuator in the splitter plate.

      Figure 4.  Two-electrode plasma synthetic actuator

    • 使用纹影系统观测等离子体合成射流对混合层的扰动过程. 纹影系统主要包括光源、高速相机、凹面镜、刀口. 纹影系统与试验段的位置如图5所示. 凹面镜直径为200 mm、焦距为2 m. 光源采用的是连续的碘钨光源. 相机的曝光时间为1 μs, 拍摄频率为30000 Hz, 拍摄的像素为1024 pixel × 688 pixel.

      Figure 5.  The schematic diagram of schlieren system

      实验使用基于纳米粒子的平面激光散射技术(nanoparticle-based planar laser scattering, NPLS)的系统来获取流场的精细结构. NPLS系统是由赵玉新等[28]基于瑞利散射原理开发出来的. NPLS系统包含有: 双腔Nd:YAG激光器, 波长为532 nm, 单次脉冲的能量为350 mJ, 脉冲宽度为6 ns; 一台跨帧像素为4008 pixel × 2672 pixel跨帧CCD相机; 一台控制激光器和相机的同步控制器; 一台纳米粒子发生器; 一台计算机. TiO2被选为示踪粒子, TiO2有效直径为42.5 nm, 松弛时间为66.3 ns. TiO2优势在于对超声速气流中小尺度的脉动有较好的跟随性. 流场图片的灰度图与纳米粒子的浓度成比例, 纳米粒子的浓度又与密度成比例, 所以流场图片的灰度值可以反映密度场.

      粒子图像测速仪(particle image velocimetry, PIV)与NPLS系统共用一套设备. 利用纳米粒子良好的跟随性可以获得较为准确的超声速流场速度分布. CCD相机的最短曝光时间间隔为0.5 μs, 根据两幅跨帧图像以及时间间隔可以得出速度场.

      NPLS/PIV的最大工作频率为2 Hz, 但是相机的曝光时间仅为6 ns, 等离子体合成射流激励器作用在流场的时间远小于1 ms. 等离子体合成射流的扰动需要一段时间之后才能传递到观测区域中间方便观测. 为满足上述的要求, NPLS/PIV需要在等离子体合成射流激励器工作一段时间之后再开启工作. 用一台信号源发生器先触发等离子体合成射流激励器, 延时一段时间触发NPLS/PIV系统. NPLS/PIV拍摄区域见图3. 实验系统的具体时序见图6.

      Figure 6.  Schematics of the experimental system sequence chart.

    3.   实验结果
    • 图7为等离子体合成射流单次脉冲的纹影图片. 图7(a)是等离子体合成射流没有工作时的状态. 当等离子体合成射流开始放电时设为T0时刻. 图7(b)为(T0 + 67 μs)时刻的纹影结果, 从图中可以看出在射流出口上游产生一道斜激波, 表明射流开始喷出. 图7(c)为(T0 + 233 μs)时刻的纹影结果, 可以看到此时的混合层与未受扰动的有所区别, 在射流出口之前激波变为正激波, 说明此时射流强度较大. 图8为单次扰动的等离子体合成射流的NPLS结果. 图8(a)是未受扰动时NPLS流场结构图像, 可以看出流场已经是湍流状态. 图8(b)为(T0 + 180 μs)时刻的NPLS结果, 可以看出等离子体合成射流诱导出了大尺度的涡结构. 但是86 mm之后由于扰动尚未传播到, 因而未形成此位置之前量级的大尺度涡结构. 图8(c)是(T0 + 230 μs)的NPLS结果, 扰动的随着气流继续向下游运动, 在扰动过后大尺度涡结构继续增长, 相较于图8(b)中涡结构尺度有所增大. 图9为等离子体合成射流扰动后的PIV平均结果, 图9(a)为未受扰动的流向平均速度场, 图9(b)为(T0 + 230 μs)时刻流向速度平均云图. 通过图9(a)(b)两幅图的对比可以看出, 在60—100 mm之间, 混合层处的流向速度分布有明显不同. 对应到图8(c)NPLS结果中, 可看出扰动在这个时刻传递到此处, 说明等离子体合成射流可以对速度场造成较大的扰动. 同时也说明经过系统精确控制, 等离子体合成射流在相同的延时条件下, 流过流场的距离较为稳定. 图9(c)为未受扰动时刻的横向速度标准差, 由于横向速度变化较大, 在混合层区域标准偏差较大. 图9(d)为(T0 + 230 μs)时刻的横向速度标准偏差, 与图9(c)对比可以看出在80—100 mm处横向速度标准偏差较大, 说明此处受扰动后横向速度脉动量加大.

      Figure 7.  Schlieren images: (a) T0 + 0 μs; (b) T0 + 67 μs; (c) T0 + 233 μs.

      Figure 8.  NPLS images of supersonic mixing layer under perturbation and unperturbation: (a) Unperturbation; (b) T0 + 180 μs; (c) T0 + 230 μs.

      Figure 9.  PIV experimental results: (a) Averaged X-velocity; (b) averaged X-velocity at T0 + 230 μs; (c) Y-velocity standard deviation; (d) Y-velocity standard deviation at T0 + 230 μs.

    4.   数值仿真
    • 由于实验获取数据较少, 对电源的要求较高, 因而采用仿真手段进行研究. 研究高频激励器布置在不同位置对超声速混合层的影响效果. 仿真对象的射流出口的为大长宽比的窄缝, 当出口的长宽比大于1∶4的时候可以看作是二维, 进而可以使用二维仿真进行研究[29]. 分别对无扰动(unperturbation)、激励器在隔板上表面(up)、激励器在隔板尾端(end)、激励器在隔板下表面(bottom)四种工况进行仿真, 物理模型见图10. 模拟频率为5 kHz, 单次释放能量为150 mJ. 假设每次释放的热量相同, 假设布置在不同位置激励器释放的热量也相同, 使用Fluent 15.0的大涡模拟, 时间精度采用的是二阶隐式, 对流通量使用三阶AUSM离散, 空间项使用三阶MUSCL离散.

      Figure 10.  Physical model: (a) Unperturbation; (b) the actuator at the upper surface of the splitter plate; (c) the actuator at the end surface of splitter plate; (d) the actuator at bottom surface of splitter plate.

      等离子体对气体加热的过程十分复杂, 本文将其简化为一个热源. 将放热过程持续时间设置为10 μs, 假设热量为恒定输出. 根据文献[30], 其释放热效率取为10%, 热源密度为

      其中${\eta _{\rm{h}}}$代表热效率, ${E_{\rm{c}}}$代表输入的能量, V代表激励器腔体的体积, $\tau $代表放电持续的时间, f代表的是激励器的频率. 上下面设置为压力远场, 上下入口采用的是压力入口, 具体参数见表1. 出口设置为压力出口. 腔体材料采用的是树脂材料, 所以将壁面条件近似设置为绝热条件.

    • 仿真模型以及网格加密示意图如图11所示, 使用结构化网格对流场进行网格划分, 对隔板上下表面进行网格加密, 隔板上下表面第一层网格为2 × 10–6 m, 以确保y+ ≤ 1, 满足大涡模拟对第一层网格的要求. 对混合层所在区域进行y方向加密. 在流场的入口以及隔板尾端进行x方向加密.

      Figure 11.  Calculation model and grid for code validation.

      使用三套网格进行网格无关性验证, grid-1网格量为179640, grid-2网格量为334804, grid-3网格量为742480. 图12为未受扰动工况下三套网格的数值仿真结果和实验结果在流向x = 150 mm处的流向速度剖面曲线. 从图12中可以看出三套网格结果相差不大, 说明满足网格无关性的要求. 本文选取grid-2网格做计算.

      Figure 12.  Certification of grid independence and code validation

      算例验证主要包括两个方面, 一是计算方法是否可以准确的仿真超声速混合层; 二是计算方法是否可以仿真等离子体合成射流对超声速流场的扰动. 对于对超声速混合层的数值仿真, 从图12中可以看出数值仿真结果与实验结果在上侧和下侧气流处略有偏差. 对于流场上侧和下侧出现偏差的原因主要是: 1)PIV系统本身存在1%左右的误差; 2)作为数值仿真边界条件的流场测量参数存在测量误差. 在流场的混合区域, 数值仿真结果与实验结果存在一定的误差. 从图7图8可以看出, 流场中存在着安装激波、隔板尾端的膨胀波以及混合层相遇产生的再附激波, 经过波系后混合层向上侧倾斜, 并且涡量增大混合更加均匀. 这样就出现了图12中的结果, 实验结果的混合区域比数值仿真结果位置偏上, 并且实验结果比数值仿结果速度曲线过渡更加平滑. 总体来说, 采用的计算方法合理且可行.

      等离子体合成射流对超声速流场扰动的算例验证, 仿真采用图10(b)所示的物理模型. 使用纹影结果和NPLS结果与数值仿真结果进行对比. 如图13所示, 在(T0 + 67 μs)时刻的数值纹影和纹影实验结果进行对比, 可以看出在射流孔的上游都产生了斜激波. 如图14所示, 将(T0 + 180 μs)时刻数值仿真密度场和NPLS结果进行对比, 可以看出扰动传递到的地方会产生较大的涡结构, 在扰动未传播到的地方, 涡结构较小. 但是数值仿真的扰动传播距离要小于实验中扰动传播的距离. 由于采用二数值仿真, 其腔体大小和出口直径不能完全反映实验工况. 激励器腔体内放电过程较为复杂, 仿真时只是将放电能量沉积过程简化为一个热源对腔体气体加热过程, 其能量传递给腔体气体的值也难以准确估算. 因此仿真与实验结果存在一定的差距. 但是数值仿真可以反映超声速混合层受等离子体合成射流扰动的基本形态和发展趋势, 可以进行定性的对比分析.

      Figure 13.  T0 + 67 μs, numerical and experimental schlierens: (a) Experimental schlieren; (b) numerical schlieren.

      Figure 14.  T0 + 180 μs, contour of density and NPLS result: (a) NPLS result; (b) contour of density.

    • 图15所示为(T0 + 555 μs)时刻瞬时数值仿真密度场, 与未受扰动的工况对比, 可以看出这三个工况涡结构都有明显的增大, 扰动已经影响到了整个流场, 诱导出连续大尺度涡结构.

      Figure 15.  Contours of density at T0 + 555 μs: (a) Unperturbation; (b) the actuator at the upper surface of the splitter plate; (c) the actuator at the end surface of the splitter plate; (d) the actuator at the bottom surface of the splitter plate.

      图16为(T0 + 75 μs)瞬时温度云图和流线仿真结果. 图16(a)中激励器在隔板上表面布置, 可以看出热气流喷出后, 形成一个虚拟型面将来流抬高, 周期性的射流喷出可以实现气流的上下摆动, 使得y方向速度脉动量增加, 有助于气流掺混均匀. 图16(b)中激励器在隔板的尾端布置, 可以看出等离子体合成射流喷出后直接作用在混合层的再附点上, 从而加快混合层失稳, 达到增强混合的效果. 并且由图16(a)图16(b)这两个图可以推知, 由于在隔板尾端布置的激励器可以直接作用在混合层上, 因而混合层对在隔板尾端布置的激励器扰动响应最快.

      Figure 16.  Simulation of the temperature and flow: (a) The actuator at the upper surface of the splitter plate; (b) the actuator at the end surface of the splitter plate

      图17为555 μs内的时均速度厚度曲线. 混合层速度厚度δ定义为归一化速度$\overline {{U}} = 0.1$$\overline {{U}} = 0.9$之间的横向距离, 归一化速度定义为[31]

      Figure 17.  Time-averaged velocity thickness of mixing layer

      可以看出有扰动工况混合层厚度都比未添加扰动工况大. 在添加扰动的工况中, 在隔板尾端布置激励器的工况混合层厚度最大. 这是由于混合层存在速度拐点, 是天然的不稳定系统, 在隔板尾端布置的激励器喷出的射流直接作用在混合层上. 此外由于仿真工况来流湍流度不高, 混合层对微小扰动较为敏感, 在隔板尾端布置的激励器不工作的时候, 腔体与上下两股气流相互作用也会诱导出大尺度涡结构, 从而增加了时均混合层速度厚度. 在隔板上下表面布置激励器的工况, 混合层厚度相差不大, 但是可以看出布置在上表面的工况混合层厚度大于布置在下表面工况的混合层厚度. 这是由于上面气流的速度以及总压低于下面气流, 上侧添加扰动更容易实现混合层厚度的增长.

    • 图18为激励器出口参数. 由于在隔板尾端外部压力较小, 喷出射流获得了较大的速度, 因此气体膨胀做功转化的动能较多, 因而出口的动量是这三个工况中最大的. 而在隔板上下表面布置的激励器, 射流与来流相互作用, 气体膨胀做功转化为动能较少. 但是由于上下两股气流的引射造成隔板尾端布置的激励器腔体内气体密度较小, 因而喷出的射流质量流量最小. 同时可以看出在隔板尾端布置激励器出口压力也小于激励器布置在隔板上下表面的工况.

      Figure 18.  The parameters of actuator outlet: (a) The mass flow rate of actuator outlet; (b) the velocity of actuator outlet; (c) the momentum rate of actuator outlet; (d) the pressure of actuator outlet.

      图19为激励器腔体内参数. 图19(a)为激励器腔体内气体密度曲线图, 从图中可以发现, 腔体内密度随着放电次数的增加而逐渐降低. 这是由于算例设置的激励器腔体是绝热壁面, 做功过后腔体内温度难以降低, 腔体内维持一定压力造成外部气体内难以回吸. 这样就导致随放电次数增多, 激励器做功能力下降. 对于高频的激励器来说, 应该采用六方氮化硼陶瓷等导热能力强的材料作为激励器腔体, 或者采用冲压式激励器[32]. 图19(b)为激励器腔体温度曲线图, 在热源释放热量相同, 腔体体积相同的情况下, 腔体内气体温度的变化与密度成反比. 由于激励器布置在不同位置造成腔体内密度不相同, 因此温度变化也不相同. 在隔板尾端布置的激励器由于气体密度最小, 所以温度升高也最高. 图19(c)为激励器腔体内压力曲线图, 可见激励器布置在隔板上下表面的工况腔体内的最大压力是相同, 而在隔板尾端布置的激励器腔体内的最大压力小于其他两个工况. 这可能是由于上下两股气流的引射, 造成腔体内密度较小, 因而最大压力要小于其他两个工况的最大压力. 同时可以看出这三个工况达到峰值压力的时间差别不大.

      Figure 19.  Parameters of actuator cavity: (a) Density of the gas in the actuator chamber; (b) temperature of the gas in the actuator chamber; (c) pressure of the gas in the actuator chamber.

    5.   结 论
    • 本文采用纹影方法研究等离子体射流扰动混合层的过程, 采用NPLS和PIV方法研究了超声速混合层受等离子体合成射流扰动后的流场特性. 采用数值仿真的方法研究了高频等离子体合成射流布置在不同位置对超声速混合层的影响, 以及布置位置不同对等离子体合成射流激励器性能的影响. 实验表明等离子体合成射流对超声速混合层扰动十分明显. 仿真结果表明高频激励器有效地增强混合层的厚度, 获得以下主要结论.

      1)激励器出口布置隔板上下表面作用机理与激励器出口布置在隔板尾端的作用机理不相同. 布置在隔板上下表面激励器先作用在来流上, 然后再影响混合层发展, 激励器出口在隔板尾端的射流作用在混合层再附点上, 加速混合层的失稳. 并且可以推知混合层对在隔板尾端布置的激励器响应最快.

      2)在激励器腔体内气体吸收的热量是在相同的前提下, 位置不同导致激励器出口的外部环境差别较大, 因而对等离子体合成射流做功能力的影响很大.

      3)高频等离子体合成射流激励器对气体回吸要求较高, 只有气体及时回吸才能将保证激励器做功能力不衰减. 因此在设计等离子体合成射流激励器时应该采用导热性能好的材料或者采用冲压式设计, 保证每次做功激励器腔体内气体密度符合要求.

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