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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2019, Vol. 40 ›› Issue (5): 122504-122504.doi: 10.7527/S1000-6893.2018.22504

• Fluid Mechanics and Flight Mechanics • Previous Articles     Next Articles

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

TONG Fulin1,2, ZHOU Guiyu1, ZHOU Hao3, ZHANG Peihong1, LI Xinliang2,3   

  1. 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:2018-07-01 Revised:2018-07-31 Online:2019-05-15 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.

Key words: shock wave/turbulent boundary layer interaction, wall shear stress, pre-multiplied power spectral density, probability density function, proper orthogonal decomposition

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