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Near-wall behaviors of oblique-shock-wave/turbulent-boundary-layer interactions

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Abstract

A direct numerical simulation (DNS) on an oblique shock wave with an incident angle of 33.2° impinging on a Mach 2.25 supersonic turbulent boundary layer is performed. The numerical results are confirmed to be of high accuracy by comparison with the reference data. Particular efforts have been made on the investigation of the near-wall behaviors in the interaction region, where the pressure gradient is so significant that a certain separation zone emerges. It is found that, the traditional linear and logarithmic laws, which describe the mean-velocity profiles in the viscous and meso sublayers, respectively, cease to be valid in the neighborhood of the interaction region, and two new laws of the wall are proposed by elevating the pressure gradient to the leading order. The new laws are inspired by the analysis on the incompressible separation flows, while the compressibility is additionally taken into account. It is verified by the DNS results that the new laws are adequate to reproduce the mean-velocity profiles both inside and outside the interaction region. Moreover, the normalization adopted in the new laws is able to regularize the Reynolds stress into an almost universal distribution even with a salient adverse pressure gradient (APG).

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Acknowledgements

The authors are grateful to Professor Xinliang LI of Institute of Mechanics, Chinese Academy of Sciences for kindly providing the DNS code. Professors Heng ZHOU and Jisheng LUO of Tianjin University are also acknowledged for their valuable discussion and suggestions. This work is carried out at the National Supercomputer Center in Tianjin, and the calculations are performed on TianHe-1 (A).

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Mingsheng Ye & Ming Dong

  2. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin, 300072, China

    Ming Dong

Authors
  1. Mingsheng Ye
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  2. Ming Dong
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Correspondence to Ming Dong.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11472189 and 11332007)

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Ye, M., Dong, M. Near-wall behaviors of oblique-shock-wave/turbulent-boundary-layer interactions. Appl. Math. Mech.-Engl. Ed. 38, 1357–1376 (2017). https://doi.org/10.1007/s10483-017-2248-6

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  • DOI: https://doi.org/10.1007/s10483-017-2248-6

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