激波/湍流边界层干扰物面剪切应力统计特性
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摘要
为了揭示激波/湍流边界层干扰区内物面剪切应力统计特性的演化规律,采用直接数值模拟方法对来流马赫数2.9、12°激波角的入射激波与平板湍流边界层相互作用问题进行了研究。通过与风洞试验数据的比较分析,验证了计算结果的可靠性。系统地探究了干扰区内物面剪切应力的典型特征,如预乘谱、概率密度分布和相干结构等。研究结果表明,分离激波的低频振荡运动对流向及展向分量的预乘谱均没有实质影响,其脉动仍以高频特征为主,低频能量变化较小。干扰区内流向剪切应力概率密度函数分布变化剧烈,分离泡内对数正态分布规律不再适用,而展向剪切应力在干扰区内与正态分布较为接近。相较于上游湍流边界层,分离泡内物面剪切应力矢量夹角与幅值的联合概率密度变化显著,峰值概率降低,峰值范围增大。此外,流向剪切应力脉动场的本征正交分解分析指出,主能量模态与分离激波的低频振荡以及下游再附边界层内的G?rtler-like流向涡结构密切相关。
To reveal the evolution of wall shear stress characteristics in the interaction region,direct numerical simulation of a reflected shock wave and turbulent boundary layer interaction for the incident shock of 12°at Mach number 2.9 is performed.The accuracy of numerical results has been validated against the experimental data and previous direct numerical simulations under matching conditions.The statistical characteristics of wall shear stress,including pre-multiplied power spectral density,probability density function and coherent structures have been analyzed in detail.Results indicate that the low-frequency motions of separated shock wave have no substantial influence on the power spectrum of streamwise and spanwise components of wall shear stress vector.The fluctuations are dominated by high-frequency content and the low-frequency energy exhibits little change.The distribution of probability density functions of streamwise wall shear stress varies dramatically through the interaction region and the law of logarithmic normal distribution is not applicable to the separation bubble,but the distribution of spanwise component is approximately of normal distribution throughout the interaction region.Compared with the upstream undisturbed turbulent boundary layer,the joint probability density function between the angle and magnitude of wall shear stress vector is significantly changed in the separation bubble,with the peak of probability decreasing and the range of maximum values increasing.The proper orthogonal decomposition analysis of the fluctuating streamwise shear stress indicates that the dominant modes are closely associated with the low-frequency oscillations of the separated shock wave and the G?rtler-like streamwise vortex structures in the reattachment boundary layer downstream.
To reveal the evolution of wall shear stress characteristics in the interaction region,direct numerical simulation of a reflected shock wave and turbulent boundary layer interaction for the incident shock of 12°at Mach number 2.9 is performed.The accuracy of numerical results has been validated against the experimental data and previous direct numerical simulations under matching conditions.The statistical characteristics of wall shear stress,including pre-multiplied power spectral density,probability density function and coherent structures have been analyzed in detail.Results indicate that the low-frequency motions of separated shock wave have no substantial influence on the power spectrum of streamwise and spanwise components of wall shear stress vector.The fluctuations are dominated by high-frequency content and the low-frequency energy exhibits little change.The distribution of probability density functions of streamwise wall shear stress varies dramatically through the interaction region and the law of logarithmic normal distribution is not applicable to the separation bubble,but the distribution of spanwise component is approximately of normal distribution throughout the interaction region.Compared with the upstream undisturbed turbulent boundary layer,the joint probability density function between the angle and magnitude of wall shear stress vector is significantly changed in the separation bubble,with the peak of probability decreasing and the range of maximum values increasing.The proper orthogonal decomposition analysis of the fluctuating streamwise shear stress indicates that the dominant modes are closely associated with the low-frequency oscillations of the separated shock wave and the G?rtler-like streamwise vortex structures in the reattachment boundary layer downstream.
引文
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[18]童福林,李欣,于长平,等.高超声速激波湍流边界层干扰直接数值模拟研究[J].力学学报,2018,50(2):197-208.TONG F L,LI X,YU C P,et al.Direct numerical simulation of hypersonic shock wave and turbulent boundary layer interactions[J].Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):197-208(in Chinese).
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[20]BOOKEY P B,WYCKHAM C,SMITS A J.Experimental investigations of Mach 3shock wave turbulent boundary layer interaction:AIAA-2005-4899[R].Reston,VA:AIAA,2005.
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[22]MARTIN M P,TAYLOR E M,WU M.A bandwidthoptimized WENO scheme for the effective direct numerical simulation of compressible turbulence[J].Journal of Computational Physics,2006,220:270-289.
[23]PIROZZOLI S,GRASSO F.Direct numerical simulation of impinging shock wave turbulent boundary layer interaction at M=2.25[J].Physics of Fluids,2006,18:065113.
[24]PIROZZOLI S,BERNARDINI M,GRASSO F.Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation[J].Journal of Fluid Mechanics,2009,657:361-393.
[25]WU X,MOIN P.Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer[J].Journal of Fluid Mechanics,2009,630:5-41.
[26]CARLOS D D,SYLVAIN L,CHRISTOS V J.Wall shear stress fluctuations:Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer[J].Physics of Fluids,2017,29:055102.
[27]HU Z W,MORFEY C L,SANDHAM N D.Wall pressure and shear stress spectra from direct simulation of channel flow[J].AIAA Journal,2006,44(7):1541-1549.
[28]WU M,MARTIN M P.Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp[J].AIAA Journal,2007,45(4):879-889.
[29]COLELLA K J,KEITH W L.Measurements and scaling of wall shear stress fluctuations[J].Experiments in Fluids,2003,34(2):253-260.
[30]BRUCKER C.Evidence of rare backflow and skin-friction critical points in near-wall turbulence using micropillar imaging[J].Physics of Fluids,2015,27:031705.
[31]JEON S,CHOI H,MOIN P.Space-time characteristics of the wall shear-stress fluctuations in a low Reynolds number channel flow[J].Physics of Fluids,1999,11:3084-3094.
[32]BERKOOZ G,HOLMES P,LUMLEY J L.The proper orthogonal decomposition in the analysis of turbulent flows[J].Annual Review of Fluid Mechanics,1993,25:539-575.
[33]PASQUARIELLO V,HICKEL S,ADAMS N A.Unsteady effects of strong shock wave/boundary layer interaction at high Reynolds number[J].Journal of Fluid Mechanics,2017,823:617-657.
[2]GAITONDE D V.Progress in shock wave/boundary layer interactions[J].Progress in Aerospace Sciences,2015,72:80-99.
[3]CLEMENS N T,NARAYANASWAMY V.Low frequency unsteadiness of shock wave turbulent boundary layer interactions[J].Annual Review of Fluid Mechanics,2014,46:469-492.
[4]SETTLES G S,FITZPATRICK T J.Detailed study of attached and separated compression corner flowfields in high Reynolds number supersonic flow[J].AIAA Journal,1979,17(6):579-585.
[5]ARDONCEAU P L.The structure of turbulence in a supersonic shock wave/boundary layer interaction[J].AIAA Journal,1984,22(9):1254-1262.
[6]SMITS A J,MUCK K C.Experimental study of three shock wave/turbulent boundary layer interaction[J].Journal of Fluid Mechanics,1987,182:291-314.
[7]ANDREOPOULOS J,MUCK K C.Some new aspects of the shock wave/boundary layer interaction in compression ramp flows[J].Journal of Fluid Mechanics,1987,180:405-428.
[8]ERENGIL M E,DOLLING D S.Correlation of separation shock motion with pressure fluctuations in the incoming boundary layer[J].AIAA Journal,1991,29(11):1868-1877.
[9]BERESH S J,CLEMENS N T,DOLLING D S.Relationship between upstream turbulent boundary layer velocity fluctuations and separation shock unsteadiness[J].AIAAJournal,2002,40(12):2412-2422.
[10]HUMBLE R A,SCARANO F.Unsteady aspects of an incident shock wave turbulent boundary layer interaction[J].Journal of Fluid Mechanics,2009,635:47-74.
[11]ADAMS N A.Direct simulation of the turbulent boundary layer along a compression ramp at M=3and Reθ=1 685[J].Journal of Fluid Mechanics,2000,420:47-83.
[12]RINGUETTE M J,WU M,MARTIN M P.Low Reynolds number effects in a Mach 3 shock and turbulent boundary layer interaction[J].AIAA Journal,2008,46(7):1884-1887.
[13]PRIEBE S,WU M,MARTIN M P.Direct numerical simulation of a reflected shock wave turbulent boundary layer interaction[J].AIAA Journal,2009,47(5):1173-1185.
[14]PRIEBE S,WU M,MARTIN M P.Low-frequency unsteadiness in shock wave turbulent boundary layer interaction[J].Journal of Fluid Mechanics,2012,699:1-49.
[15]LI X L,FU D X,MA Y W,et al.Direct numerical simulation of shock/turbulent boundary layer interaction in a supersonic compression ramp[J].Science China Physics,Mechanics and Astronomy,2010,53(9):1651-1658.
[16]TONG F L,YU C P,TANG Z G,et al.Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects[J].Computers and Fluids,2017,149:56-69.
[17]TONG F L,TANG Z G,YU C P,et al.Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls[J].Journal of Turbulence,2017,18(6):569-588.
[18]童福林,李欣,于长平,等.高超声速激波湍流边界层干扰直接数值模拟研究[J].力学学报,2018,50(2):197-208.TONG F L,LI X,YU C P,et al.Direct numerical simulation of hypersonic shock wave and turbulent boundary layer interactions[J].Chinese Journal of Theoretical and Applied Mechanics,2018,50(2):197-208(in Chinese).
[19]MURTHY V S,ROSE W C.Wall shear stress measurements in a shock-wave boundary layer interaction[J].AIAA Journal,1978,16(7):667-672.
[20]BOOKEY P B,WYCKHAM C,SMITS A J.Experimental investigations of Mach 3shock wave turbulent boundary layer interaction:AIAA-2005-4899[R].Reston,VA:AIAA,2005.
[21]童福林,唐志共,李新亮,等.压缩拐角激波与旁路转捩边界层干扰数值研究[J].航空学报,2016,37(12):3588-3604.TONG F L,TANG Z G,LI X L,et al.Numerical study of shock wave and bypass transitional boundary layer interaction in a supersonic compression ramp[J].Acta Aeronautica et Astronautica Sinica,2016,37(12):3588-3604(in Chinese).
[22]MARTIN M P,TAYLOR E M,WU M.A bandwidthoptimized WENO scheme for the effective direct numerical simulation of compressible turbulence[J].Journal of Computational Physics,2006,220:270-289.
[23]PIROZZOLI S,GRASSO F.Direct numerical simulation of impinging shock wave turbulent boundary layer interaction at M=2.25[J].Physics of Fluids,2006,18:065113.
[24]PIROZZOLI S,BERNARDINI M,GRASSO F.Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation[J].Journal of Fluid Mechanics,2009,657:361-393.
[25]WU X,MOIN P.Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer[J].Journal of Fluid Mechanics,2009,630:5-41.
[26]CARLOS D D,SYLVAIN L,CHRISTOS V J.Wall shear stress fluctuations:Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer[J].Physics of Fluids,2017,29:055102.
[27]HU Z W,MORFEY C L,SANDHAM N D.Wall pressure and shear stress spectra from direct simulation of channel flow[J].AIAA Journal,2006,44(7):1541-1549.
[28]WU M,MARTIN M P.Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp[J].AIAA Journal,2007,45(4):879-889.
[29]COLELLA K J,KEITH W L.Measurements and scaling of wall shear stress fluctuations[J].Experiments in Fluids,2003,34(2):253-260.
[30]BRUCKER C.Evidence of rare backflow and skin-friction critical points in near-wall turbulence using micropillar imaging[J].Physics of Fluids,2015,27:031705.
[31]JEON S,CHOI H,MOIN P.Space-time characteristics of the wall shear-stress fluctuations in a low Reynolds number channel flow[J].Physics of Fluids,1999,11:3084-3094.
[32]BERKOOZ G,HOLMES P,LUMLEY J L.The proper orthogonal decomposition in the analysis of turbulent flows[J].Annual Review of Fluid Mechanics,1993,25:539-575.
[33]PASQUARIELLO V,HICKEL S,ADAMS N A.Unsteady effects of strong shock wave/boundary layer interaction at high Reynolds number[J].Journal of Fluid Mechanics,2017,823:617-657.