Fluid Mechanics and Flight Mechanics

Statistical characteristics of wall shear stress in shock wave and turbulent boundary layer interactions

  • TONG Fulin ,
  • ZHOU Guiyu ,
  • ZHOU Hao ,
  • ZHANG Peihong ,
  • LI Xinliang
Expand
  • 1. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
    2. Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
    3. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2018-07-01

  Revised date: 2018-07-31

  Online published: 2018-08-27

Supported by

National Natural Science Foundation of China (91441103, 11372330, 11472278); National Key Research and Development Program of China (2016YFA0401200)

Abstract

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 Görtler-like streamwise vortex structures in the reattachment boundary layer downstream.

Cite this article

TONG Fulin , ZHOU Guiyu , ZHOU Hao , ZHANG Peihong , LI Xinliang . Statistical characteristics of wall shear stress in shock wave and turbulent boundary layer interactions[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019 , 40(5) : 122504 -122504 . DOI: 10.7527/S1000-6893.2018.22504

References

[1] DOLLING D S. Fifty years of shock-wave/boundary-layer interaction research:What next?[J]. AIAA Journal, 2001, 39(8):1517-1530.
[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]. AIAA Journal, 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=3 and 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 3 shock 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 bandwidth-optimized 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.
Outlines

/