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壁面局部吹吸边界层感受性的数值研究

陆昌根 沈露予

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壁面局部吹吸边界层感受性的数值研究

陆昌根, 沈露予

Numerical study on boundary-layer receptivity with localized wall blowing/suction

Lu Chang-Gen, Shen Lu-Yu
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  • 目前理论、实验以及数值模拟主要研究自由来流中的小扰动与壁面局部粗糙相互作用激发边界层感受性问题. 但是, 针对自由来流湍流与壁面局部吹吸相互作用诱导边界层感受性的相关报道甚少. 本文采用直接数值模拟和快速傅里叶变换的方法, 数值研究了二维平板壁面具有局部吹吸的边界层感受性问题. 结果发现, 在二维边界层内能找到一组被激发产生的Tollmien-Schlichting(T-S)波波包的包络序列以及从波包中能够分离出一组稳定的、中性的和不稳定的T-S波, 证明了二维边界层内感受性现象的存在性. 经数值计算获得了T-S波波包传播的群速度; 并建立了自由来流湍流强度、壁面局部吹吸强度和长度与二维边界层感受性之间的关系, 获得了与Dietz感受性实验相类似的结论. 另外, 还发现在自由来流湍流与壁面局部吹、吸相互作用下能诱导二维边界层内产生相位相反的T-S波. 依据这一理论机理来优化设计局部吹吸装置, 不但能促使层流向湍流转捩的提前, 也可以延迟转捩过程的发生, 达到控制湍流运动的目的.
    Most of previous studies focused on the boundary-layer receptivity to the convected disturbances in the free stream interacting with localized wall roughness. Whereas the research on the boundary-layer receptivity induced by localized blowing or localized suction is relatively few. In this paper, we investigate two-dimensional boundary-layer receptivity induced by localized blowing/suction within free-stream turbulence through using direct numerical simulation and fast Fourier transformation. High-order compact finite difference schemes in the y-direction, fast Fourier transformation in the x-direction, and a Runge-Kutta scheme in time domain are used to solve the Navier-Stokes equations. The numerical results show that Tollmien-Schlichting (T-S) wave packets are excited by the free-stream turbulence interacting with localized blowing in the two-dimensional boundary layer, which are superposed by a group of stable, neutral and unstable T-S waves. The dispersion relations, growth rates, amplitude distributions and phase distributions of the excited waves accord well with theoretical solutions of the linear stability theory, thus confirming the existence of the boundary-layer receptivity. And the frequencies of the instability waves are between the upper and lower branches of the neutral stability curves. According to the evolutions of the wave packets, the positions of peaks and valleys are tracked over time to calculate the propagation speed by taking the average. The propagation speeds of the wave packets are approximately one-third of the free-stream velocity, which are in accordance with Dietz's measurements. The propagation speeds of wave packets are also close to the phase speeds of the most unstable waves for the numerical results. The relations of the receptivity response to the forcing amplitude, the blowing intensity, and the blowing width are found to be linear, when the forcing amplitude and the blowing intensity are less than 1% free-steam velocity amplitude and 0.01, respectively. And the maximum amplitudes of the T-S waves can be excited while the blowing length is equal to the resonant wavelength /(TS-FS), where TS is the wave-number of the T-S wave, and FS is the wave-number of the forcing disturbance. These results are similar to those given by Dietz [Dietz A J 1999 J. Fluid Mech. 378 291]. Additionally, T-S waves with the same dispersion relations but opposite phases are generated by localized blowing and localized suction respectively, and the amplitudes of the T-S waves excited by localized blowing are nearly 15% greater than those by localized suction under the same condition. According to this theory, an optimal design of localized suction device is able to enhance or delay the laminar-turbulent transition for turbulent control.
      通信作者: 陆昌根, cglu@nuist.edu.cn;shenluyu99@foxmail.com ; 沈露予, cglu@nuist.edu.cn;shenluyu99@foxmail.com
    • 基金项目: 国家自然科学基金(批准号: 11172143)、江苏省研究生创新计划(批准号: CXZZ130518)和江苏高校优势学科建设工程资助的课题.
      Corresponding author: Lu Chang-Gen, cglu@nuist.edu.cn;shenluyu99@foxmail.com ; Shen Lu-Yu, cglu@nuist.edu.cn;shenluyu99@foxmail.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11172143), the Research Innovation Program for College Graduates of Jiangsu Province, China (Grant No. CXZZ130518), and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.
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    [2]

    Gong A L, Li R Q, Li C B 2002 Acta Phys. Sin. 51 1068 (in Chinese) [龚安龙, 李睿劬, 李存标 2002 物理学报 51 1068]

    [3]

    Chen L, Tang D B 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌 2011 物理学报 60 094702]

    [4]

    Hu H B, Du P, Huang S H, Wang Y 2013 Chin. Phys. B 22 074703

    [5]

    Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703

    [6]

    Saric W S, Reed H L, Kerschen E J 2002 Annu. Rev. Fluid Mech. 34 291

    [7]

    Kurz H B E, Kloker M J 2014 J. Fluid Mech. 755 62

    [8]

    Ustinov M V 2013 Fluid Dynam. 48 621

    [9]

    Ustinov M V 2014 Fluid Dynam. 49 468

    [10]

    Morkovin M V 1969 On the Many Faces of Transition Viscous Drag Reduction (New York: Springer) pp1-31

    [11]

    Goldstein M E 1983 J. Fluid Mech. 127 59

    [12]

    Goldstein M E 1985 J. Fluid Mech. 154 509

    [13]

    Ruban A I 1984 Fluid Dynam. 19 709

    [14]

    Kerschen E J 1990 Appl. Mech. Rev. 43 152

    [15]

    Zavol'Skii N A, Reutov V P, Rybushkina G V 1983 J. Appl. Mech. Tech. Phys. 24 355

    [16]

    Duck P W, Ruban A I, Zhikharev C N 1996 J. Fluid Mech. 312 341

    [17]

    Dietz A J 1996 AIAA P. 96 2083

    [18]

    Dietz A J 1998 AIAA J. 36 1171

    [19]

    Dietz A J 1999 J. Fluid Mech. 378 291

    [20]

    Wu X S 2001 J. Fluid Mech. 431 91

    [21]

    Wu X S 2002 J. Fluid Mech. 453 289

    [22]

    Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292

    [23]

    Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180

    [24]

    Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873

    [25]

    Zhang Y, Zhou H 2005 Appl. Math. Mech. 26 547

    [26]

    Ricco P 2009 J. Fluid Mech. 638 267

  • [1]

    Li C B, Fu S 2000 Chin. Phys. 9 508

    [2]

    Gong A L, Li R Q, Li C B 2002 Acta Phys. Sin. 51 1068 (in Chinese) [龚安龙, 李睿劬, 李存标 2002 物理学报 51 1068]

    [3]

    Chen L, Tang D B 2011 Acta Phys. Sin. 60 094702 (in Chinese) [陈林, 唐登斌 2011 物理学报 60 094702]

    [4]

    Hu H B, Du P, Huang S H, Wang Y 2013 Chin. Phys. B 22 074703

    [5]

    Wang W, Guan X L, Jiang N 2014 Chin. Phys. B 23 104703

    [6]

    Saric W S, Reed H L, Kerschen E J 2002 Annu. Rev. Fluid Mech. 34 291

    [7]

    Kurz H B E, Kloker M J 2014 J. Fluid Mech. 755 62

    [8]

    Ustinov M V 2013 Fluid Dynam. 48 621

    [9]

    Ustinov M V 2014 Fluid Dynam. 49 468

    [10]

    Morkovin M V 1969 On the Many Faces of Transition Viscous Drag Reduction (New York: Springer) pp1-31

    [11]

    Goldstein M E 1983 J. Fluid Mech. 127 59

    [12]

    Goldstein M E 1985 J. Fluid Mech. 154 509

    [13]

    Ruban A I 1984 Fluid Dynam. 19 709

    [14]

    Kerschen E J 1990 Appl. Mech. Rev. 43 152

    [15]

    Zavol'Skii N A, Reutov V P, Rybushkina G V 1983 J. Appl. Mech. Tech. Phys. 24 355

    [16]

    Duck P W, Ruban A I, Zhikharev C N 1996 J. Fluid Mech. 312 341

    [17]

    Dietz A J 1996 AIAA P. 96 2083

    [18]

    Dietz A J 1998 AIAA J. 36 1171

    [19]

    Dietz A J 1999 J. Fluid Mech. 378 291

    [20]

    Wu X S 2001 J. Fluid Mech. 431 91

    [21]

    Wu X S 2002 J. Fluid Mech. 453 289

    [22]

    Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292

    [23]

    Shen L Y, Lu C G, Wu W G, Xue S F 2015 Add. Appl. Math. Mech. 7 180

    [24]

    Lu C G, Cao W D, Zhang Y M, Guo J T 2008 P. Nat. Sci. 18 873

    [25]

    Zhang Y, Zhou H 2005 Appl. Math. Mech. 26 547

    [26]

    Ricco P 2009 J. Fluid Mech. 638 267

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出版历程
  • 收稿日期:  2015-03-31
  • 修回日期:  2015-07-01
  • 刊出日期:  2015-11-05

壁面局部吹吸边界层感受性的数值研究

    基金项目: 国家自然科学基金(批准号: 11172143)、江苏省研究生创新计划(批准号: CXZZ130518)和江苏高校优势学科建设工程资助的课题.

摘要: 目前理论、实验以及数值模拟主要研究自由来流中的小扰动与壁面局部粗糙相互作用激发边界层感受性问题. 但是, 针对自由来流湍流与壁面局部吹吸相互作用诱导边界层感受性的相关报道甚少. 本文采用直接数值模拟和快速傅里叶变换的方法, 数值研究了二维平板壁面具有局部吹吸的边界层感受性问题. 结果发现, 在二维边界层内能找到一组被激发产生的Tollmien-Schlichting(T-S)波波包的包络序列以及从波包中能够分离出一组稳定的、中性的和不稳定的T-S波, 证明了二维边界层内感受性现象的存在性. 经数值计算获得了T-S波波包传播的群速度; 并建立了自由来流湍流强度、壁面局部吹吸强度和长度与二维边界层感受性之间的关系, 获得了与Dietz感受性实验相类似的结论. 另外, 还发现在自由来流湍流与壁面局部吹、吸相互作用下能诱导二维边界层内产生相位相反的T-S波. 依据这一理论机理来优化设计局部吹吸装置, 不但能促使层流向湍流转捩的提前, 也可以延迟转捩过程的发生, 达到控制湍流运动的目的.

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