高超音速尖锥边界层转捩的多尺度互相关谱分析
|
摘要
高超音速边界层的不稳定性和转捩是航空航天的重要难题之一。为了深入的研究边界层的扰动和流动特性,在高超音速炮风洞中,对自由来流马赫数为6,攻角为0°,半锥角为5°的尖锥,同时利用分布在尖锥一条母线上的7个铂薄膜热电阻传感器精密测量其壁面脉动热流。本文对测量得到的壁面脉动热流信号进行多尺度连续小波变换,在小波分析的基础上对信号的能谱,双谱和互双谱进行计算,并抽取条件相位平均波形,分析不稳定扰动的细节发展。
通过对壁面脉动热流信号进行连续小波变换,清楚的辨识到了在高超音速流动中的第一模态和第二模态的频率特征,并发现第二模态的特征频率在整个流动一直存在且越来越多;虽然在小波系数等值线谱中发现第二模态特征频率一直出现,但是通过能谱分析发现流动开始时第二模态扰动的能量并不强,而是第一模态的谐波起主导作用,直到最后一个位置第二模态的能量才占主导;从双谱分析中观察到,初期第一二模态同时影响高超音速流动,随着边界层的发展,两个模态的影响都在增长,但是第二模态影响的区域更大;互双谱分析发现,各个特征频率之间的相位耦合作用明显,第二模态的特征频率的影响力也是一个从弱到强的过程,这与能谱分析和双谱分析中得到的结论相一致;最后用条件相位平均的办法抽取了脉动信号中的扰动波,并通过能量谱的方法观察扰动波发展的细节,发现扰动波形的幅值先增长后降低,还发现扰动波的频率主要集中在频率200 - 400KHz之间,这印证了小波系数等值图中第二模态一直存在且越来越多的观点。
通过本文的研究发现,小波分析对高超音速流动中的第一模态和第二模态的特征的辨识是非常有效的方法,而通过基于连续小波变换的相关谱分析和抽取条件相位平均波形可以对第一二模态特征和不稳定扰动的细节发展有更深入的理解。
Hypersonic boundary layer instability and transition is one of the most important problems to aeronautic and astronautic. The experiment had been devoted to learn more about the characters and the disturbances in the boundary layer. A model with 5-degree half-angle sharp cone was tested in a hypersonic gun tunnel at free-stream Mach number 6. The instantaneous fluctuating surface-thermal-flux signals were gained with 7 Pt-thin-film thermocouple sensors, which are located along the same generatrix on the sharp cone surface. The fluctuating surface-thermal-flux signals have been investigated using the wavelet analysis. The power spectrum, bispectrum and cross-bispectrum which are based on the wavelet transformation have been investigated. The conditional phase-averaging waveforms extracted were using for providing developing details of the instable disturbance in spectrum space.
The first-mode disturbance and the second-mode disturbance were observed clearly in the wavelet analysis. Although the second-mode disturbances are present all through the flow, its power isn’t the highest and the harmonic of the first-mode disturbance dominates in the initial of the flow. At the last station, the power of the second-mode disturbance are dominance. From the bispectrum analysis, the second-mode disturbance affect the hypersonic flow with together the first-mode disturbance at early stage. With the develop of the boundary layer, the effects of two modes both increase, but the effect of the second-mode is greater. The cross-bispectrum analysis show that phase-locked interactions between every frequency are apparent, and the effects of the second-mode disturbances are from slender to strong, which are consistent with the results of power spectrum and bispectrum. The power spectrum calculated for the extracted instable disturbance signals provides developing details of the instable disturbance in spectrum space. It is observed that the magnitude of disturbance waveforms increase in the initial of the flow and decrease in the middle stage. The frequence of disturbance waveforms is from 200 khz to 400 khz, which is as same as the conclusion of Wavelet coefficients magnitude contour.
In the studying of this paper, it is apparent that wavelet transformation techniques provide a new method to identify the characters of the first-mode and the second-mode disturbance in a hypersonic flow. And the correlation spectrum and conditional phase-averaging waveforms extracted which are based on the wavelet transformation show that more profound understanding about the first-mode disturbance , the second-mode disturbance and instable disturbance waveforms.
通过对壁面脉动热流信号进行连续小波变换,清楚的辨识到了在高超音速流动中的第一模态和第二模态的频率特征,并发现第二模态的特征频率在整个流动一直存在且越来越多;虽然在小波系数等值线谱中发现第二模态特征频率一直出现,但是通过能谱分析发现流动开始时第二模态扰动的能量并不强,而是第一模态的谐波起主导作用,直到最后一个位置第二模态的能量才占主导;从双谱分析中观察到,初期第一二模态同时影响高超音速流动,随着边界层的发展,两个模态的影响都在增长,但是第二模态影响的区域更大;互双谱分析发现,各个特征频率之间的相位耦合作用明显,第二模态的特征频率的影响力也是一个从弱到强的过程,这与能谱分析和双谱分析中得到的结论相一致;最后用条件相位平均的办法抽取了脉动信号中的扰动波,并通过能量谱的方法观察扰动波发展的细节,发现扰动波形的幅值先增长后降低,还发现扰动波的频率主要集中在频率200 - 400KHz之间,这印证了小波系数等值图中第二模态一直存在且越来越多的观点。
通过本文的研究发现,小波分析对高超音速流动中的第一模态和第二模态的特征的辨识是非常有效的方法,而通过基于连续小波变换的相关谱分析和抽取条件相位平均波形可以对第一二模态特征和不稳定扰动的细节发展有更深入的理解。
Hypersonic boundary layer instability and transition is one of the most important problems to aeronautic and astronautic. The experiment had been devoted to learn more about the characters and the disturbances in the boundary layer. A model with 5-degree half-angle sharp cone was tested in a hypersonic gun tunnel at free-stream Mach number 6. The instantaneous fluctuating surface-thermal-flux signals were gained with 7 Pt-thin-film thermocouple sensors, which are located along the same generatrix on the sharp cone surface. The fluctuating surface-thermal-flux signals have been investigated using the wavelet analysis. The power spectrum, bispectrum and cross-bispectrum which are based on the wavelet transformation have been investigated. The conditional phase-averaging waveforms extracted were using for providing developing details of the instable disturbance in spectrum space.
The first-mode disturbance and the second-mode disturbance were observed clearly in the wavelet analysis. Although the second-mode disturbances are present all through the flow, its power isn’t the highest and the harmonic of the first-mode disturbance dominates in the initial of the flow. At the last station, the power of the second-mode disturbance are dominance. From the bispectrum analysis, the second-mode disturbance affect the hypersonic flow with together the first-mode disturbance at early stage. With the develop of the boundary layer, the effects of two modes both increase, but the effect of the second-mode is greater. The cross-bispectrum analysis show that phase-locked interactions between every frequency are apparent, and the effects of the second-mode disturbances are from slender to strong, which are consistent with the results of power spectrum and bispectrum. The power spectrum calculated for the extracted instable disturbance signals provides developing details of the instable disturbance in spectrum space. It is observed that the magnitude of disturbance waveforms increase in the initial of the flow and decrease in the middle stage. The frequence of disturbance waveforms is from 200 khz to 400 khz, which is as same as the conclusion of Wavelet coefficients magnitude contour.
In the studying of this paper, it is apparent that wavelet transformation techniques provide a new method to identify the characters of the first-mode and the second-mode disturbance in a hypersonic flow. And the correlation spectrum and conditional phase-averaging waveforms extracted which are based on the wavelet transformation show that more profound understanding about the first-mode disturbance , the second-mode disturbance and instable disturbance waveforms.
引文
[1]周恒,关于转捩和湍流的研究,2003空气动力学前言研究论文集,87～92
[2] MaslovA A, Shiplyuk A N, Bountin D A , Sidorenko A A . Mach 6 boundary-layer stability experiments on sharp and blunted cones [J]. J Spacecraft Rockets , 2006, 43: 71～76
[3] Chokani N. Nonlinear spectral dynamics of hypersonic laminar boundary layer flow [J]. Phys Fluids , 1999, 11 : 3846～3851
[4] Whitehead A., NASP aerodynamics, AIAA Paper No.89-5013, July 1989
[5] Ericsson, L.E.: Effect of boundary layer transition on vehicle dynamics. J. Spacecr. Rocket. 6, 1404–1409 (1969)
[6] Martelluci, A., Neff, R.S.: The influence of asymmetric transition on re-entry vehicle motion. AIAA Paper No. 70-987 (1970)
[7]Holden, M.S.: Studies of the effects of transitional and turbulent boundary layers on the aerodynamic performance of hypersonic re-entry vehicles in high Reynolds number flows. Calspan Report AB-5834-A-2 (1978)
[8]Reed H.L., Saric W.S., Stability of three-dimensional boundary layers. Annu, Rev. Fluid Mech, 1989, 21:235～284.
[9] Finley D.,Hypersonic Aerodynamics Considerations and Challenges,AIAA Paper No.90-5222,October 1990
[10] Mack, L. M. 1984 Boundary layer stability theory. Special course on stability and transition of laminar flow(ed. R. Michel),AGARD Rep.709,pp.3-1–3-81.
[11] Gushchin V.R., Fedorov A.V., Asymptotic analysis of inviscid perturbations in a supersonic boundary layer, Zhurnal Prikl. Mekh. i Tekh.Fiz.,1989,1:69-75(in Russian).
[12] Malik M.R.,eMalik: A New Spatial Stability Analysis Program for Transition Prediction Using the e N method, High Technology Corporation Report No.HTC-9203, Hampton, VA, May 1992.
[13] Stetson K.F., Kimmel R.L., On hypersonic boundary layer stability,AIAA Paper, No.92-0737, January 1992
[14] Malik M.R., Hypersonic flight transition data analysis using parabolized stability equations with chemistry effects. J Spacecraft Rockets, 2003, 40(3):332～344
[15]黄章峰,曹伟,周恒。超音速平板边界层转捩中层流突变为湍流的机理—时间模式,中国科学G辑, 2005
[16] DiCristina V., Three Dimensional Laminar Boundary-Layer Transition on a Sharp 8°Cone at Mach 10, AIAA Journal,1970
[17] Kendall,J.M.,Wind tunnel experiments relating to supersonic and hypersonic boundary-layer transition. AIAA J.13(3),290-299(1975)
[18] Demetriades A.,Hypersonic viscous flow over a slender cone.PartⅢ:Laminar instability and transition.AIAA Paper No.74-535(1974)
[19]Stetson K.F.,Thompson E.R.,Donaldson J.C.,Siler,L.G.,Laminar boundary layer stability experiments on a cone at Mach 8. Part 1: sharp cone.AIAA Paper No.83-1761 (1983)
[20] Kimmel R.,Demetriades A.,Donaldson J.,Space-time correlation measurements in a hypersonic transitional boundary layer.AIAA Paper No.95-2292(1995)
[21] Lysenko V.I., Maslov A.A.,The effect of cooling on supersonic boundary-layer stability.J. Fluid Mech.147,38–52(1984)
[22] Shiplyuk A.N., Bountin D.A., Maslov A.A., Chokani N.,Subharmonic resonances in hypersonic boundary layers.AIAA Paper No.2003-0787 (2003)
[23] Pate S.R.,Dominance of radiated aerodynamic noise on boundarylayer transition in supersonic-hypersonic wind tunnels-theory and application.AEDC-TR-77-107(1978)
[24] Stetson K.F., Thompson E.R., Donaldson J.C., and Siler L.G., Laminar Boundary Layer Stability Experiments on a Cone at Mach 8, Part 3:Sharp Cone at Angle of Attack, AIAA Paper No.85-0492, January 1985
[25] Doggett G.P., Chokani N., Wilkinson S.P., Hypersonic boundary-layer stability experiments on a flared-cone model at angle of attack in a quiet wind tunnel, AIAA Paper No.1997-0557, 1997
[26] Chui C.K., An introduction to Wavelets, Academic Press, Boston, 1992
[27] Farge M., Wavelet Transforms and their Applications to Turbulence, Annu.Rev.Fluid Mech., 1992, 24:395～457
[28] Lewalle J., Wavelet Analysis of Experimental Data: Some Methods and the Underlying Physics, AIAA Paper 94-2281, June 1994
[29] Van, Milligen, B. Ph.; Sanchez, E.; Estrada, T.; Hidalgo, C.; Branas, B.; Carreras, B.; Garcia, L. Wavelet bicoherence:a new turbulence analysis tool,American Inst of Physics,1995
[30] Ndaona Chokani,VITA measurements of transition in transitional hypersonic boundary layer flows, Experiments in Fluids (2005) 38: 440–448
[31] Ndaona Chokani, Nonlinear evolution of Mack modes in a hypersonic boundary layer, Physics of fluids 17, 014102 (2005)
[32] Ndaona Chokani, Nonlinear spectral dynamics of hypersonic laminar boundary layer flow, Physics of fluids(1999)
[33] Ndaona Chokani, Transient Nonlinear Interactions in a Hypersonic Boundary Layer, AIAA 2002-0154
[34] Blackwelder RF,Kaplan RE,On the wall structure of the turbulent boundary layer, J Fluid Mech 76:89-112
[35] Robinson SK, Space-time correlation measurements in a compressible turbulent boundary layer, AIAA paper 86-1130
[36] Spina EF, Smits AJ,Organized structures in a compressible turbulent boundary layer, J Fluid Mech 182:85-109
[37] Spina EF, Donovan JF,Smits AJ, On the structure of high-Reynolds-number supersonic turbulent boundary layers, J Fluid Mech 222:293-327
[38]Bogard DG,Tiederman WG,Burst detection with single-point velocity measurements,J Fluid Mech 162:389-413
[39]王化祥,自动检测技术,北京:化学工业出版社,2009,129～131
[40]Liu Jian-hua, Jiang Nan, Two phases of coherent structure motions in turbulent boundary layer, Chinese Phys.Lett., 2007, 24(9): 2617- 2620,SCI:203FS,Impact Factor:0.812
[41]隋向坤,平板湍流边界层外区卡门涡街扰动的实验研究,硕士论文,天津大学,2009.6
[2] MaslovA A, Shiplyuk A N, Bountin D A , Sidorenko A A . Mach 6 boundary-layer stability experiments on sharp and blunted cones [J]. J Spacecraft Rockets , 2006, 43: 71～76
[3] Chokani N. Nonlinear spectral dynamics of hypersonic laminar boundary layer flow [J]. Phys Fluids , 1999, 11 : 3846～3851
[4] Whitehead A., NASP aerodynamics, AIAA Paper No.89-5013, July 1989
[5] Ericsson, L.E.: Effect of boundary layer transition on vehicle dynamics. J. Spacecr. Rocket. 6, 1404–1409 (1969)
[6] Martelluci, A., Neff, R.S.: The influence of asymmetric transition on re-entry vehicle motion. AIAA Paper No. 70-987 (1970)
[7]Holden, M.S.: Studies of the effects of transitional and turbulent boundary layers on the aerodynamic performance of hypersonic re-entry vehicles in high Reynolds number flows. Calspan Report AB-5834-A-2 (1978)
[8]Reed H.L., Saric W.S., Stability of three-dimensional boundary layers. Annu, Rev. Fluid Mech, 1989, 21:235～284.
[9] Finley D.,Hypersonic Aerodynamics Considerations and Challenges,AIAA Paper No.90-5222,October 1990
[10] Mack, L. M. 1984 Boundary layer stability theory. Special course on stability and transition of laminar flow(ed. R. Michel),AGARD Rep.709,pp.3-1–3-81.
[11] Gushchin V.R., Fedorov A.V., Asymptotic analysis of inviscid perturbations in a supersonic boundary layer, Zhurnal Prikl. Mekh. i Tekh.Fiz.,1989,1:69-75(in Russian).
[12] Malik M.R.,eMalik: A New Spatial Stability Analysis Program for Transition Prediction Using the e N method, High Technology Corporation Report No.HTC-9203, Hampton, VA, May 1992.
[13] Stetson K.F., Kimmel R.L., On hypersonic boundary layer stability,AIAA Paper, No.92-0737, January 1992
[14] Malik M.R., Hypersonic flight transition data analysis using parabolized stability equations with chemistry effects. J Spacecraft Rockets, 2003, 40(3):332～344
[15]黄章峰,曹伟,周恒。超音速平板边界层转捩中层流突变为湍流的机理—时间模式,中国科学G辑, 2005
[16] DiCristina V., Three Dimensional Laminar Boundary-Layer Transition on a Sharp 8°Cone at Mach 10, AIAA Journal,1970
[17] Kendall,J.M.,Wind tunnel experiments relating to supersonic and hypersonic boundary-layer transition. AIAA J.13(3),290-299(1975)
[18] Demetriades A.,Hypersonic viscous flow over a slender cone.PartⅢ:Laminar instability and transition.AIAA Paper No.74-535(1974)
[19]Stetson K.F.,Thompson E.R.,Donaldson J.C.,Siler,L.G.,Laminar boundary layer stability experiments on a cone at Mach 8. Part 1: sharp cone.AIAA Paper No.83-1761 (1983)
[20] Kimmel R.,Demetriades A.,Donaldson J.,Space-time correlation measurements in a hypersonic transitional boundary layer.AIAA Paper No.95-2292(1995)
[21] Lysenko V.I., Maslov A.A.,The effect of cooling on supersonic boundary-layer stability.J. Fluid Mech.147,38–52(1984)
[22] Shiplyuk A.N., Bountin D.A., Maslov A.A., Chokani N.,Subharmonic resonances in hypersonic boundary layers.AIAA Paper No.2003-0787 (2003)
[23] Pate S.R.,Dominance of radiated aerodynamic noise on boundarylayer transition in supersonic-hypersonic wind tunnels-theory and application.AEDC-TR-77-107(1978)
[24] Stetson K.F., Thompson E.R., Donaldson J.C., and Siler L.G., Laminar Boundary Layer Stability Experiments on a Cone at Mach 8, Part 3:Sharp Cone at Angle of Attack, AIAA Paper No.85-0492, January 1985
[25] Doggett G.P., Chokani N., Wilkinson S.P., Hypersonic boundary-layer stability experiments on a flared-cone model at angle of attack in a quiet wind tunnel, AIAA Paper No.1997-0557, 1997
[26] Chui C.K., An introduction to Wavelets, Academic Press, Boston, 1992
[27] Farge M., Wavelet Transforms and their Applications to Turbulence, Annu.Rev.Fluid Mech., 1992, 24:395～457
[28] Lewalle J., Wavelet Analysis of Experimental Data: Some Methods and the Underlying Physics, AIAA Paper 94-2281, June 1994
[29] Van, Milligen, B. Ph.; Sanchez, E.; Estrada, T.; Hidalgo, C.; Branas, B.; Carreras, B.; Garcia, L. Wavelet bicoherence:a new turbulence analysis tool,American Inst of Physics,1995
[30] Ndaona Chokani,VITA measurements of transition in transitional hypersonic boundary layer flows, Experiments in Fluids (2005) 38: 440–448
[31] Ndaona Chokani, Nonlinear evolution of Mack modes in a hypersonic boundary layer, Physics of fluids 17, 014102 (2005)
[32] Ndaona Chokani, Nonlinear spectral dynamics of hypersonic laminar boundary layer flow, Physics of fluids(1999)
[33] Ndaona Chokani, Transient Nonlinear Interactions in a Hypersonic Boundary Layer, AIAA 2002-0154
[34] Blackwelder RF,Kaplan RE,On the wall structure of the turbulent boundary layer, J Fluid Mech 76:89-112
[35] Robinson SK, Space-time correlation measurements in a compressible turbulent boundary layer, AIAA paper 86-1130
[36] Spina EF, Smits AJ,Organized structures in a compressible turbulent boundary layer, J Fluid Mech 182:85-109
[37] Spina EF, Donovan JF,Smits AJ, On the structure of high-Reynolds-number supersonic turbulent boundary layers, J Fluid Mech 222:293-327
[38]Bogard DG,Tiederman WG,Burst detection with single-point velocity measurements,J Fluid Mech 162:389-413
[39]王化祥,自动检测技术,北京:化学工业出版社,2009,129～131
[40]Liu Jian-hua, Jiang Nan, Two phases of coherent structure motions in turbulent boundary layer, Chinese Phys.Lett., 2007, 24(9): 2617- 2620,SCI:203FS,Impact Factor:0.812
[41]隋向坤,平板湍流边界层外区卡门涡街扰动的实验研究,硕士论文,天津大学,2009.6