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Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

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Abstract

The prediction on small disturbance propagation in complex three-dimensional (3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory (LST) with the equivalent spanwise wavenumber correction (ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

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Authors and Affiliations

  1. Laboratory for High-Speed Aerodynamics, Tianjin University, Tianjin, 300072, China

    Runjie Song & Jianxin Liu

  2. Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, 621900, Sichuan Province, China

    Shaolong Zhang

Authors
  1. Runjie Song
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  2. Shaolong Zhang
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  3. Jianxin Liu
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Corresponding author

Correspondence to Jianxin Liu.

Additional information

Project supported by the National Key Research and Development (R&D) Program of China (No. 2016YFA0401200) and the National Natural Science Foundation of China (Nos. 11402167, 11332007, 11672204, 11672205, and 11732011)

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Song, R., Zhang, S. & Liu, J. Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers. Appl. Math. Mech.-Engl. Ed. 40, 407–420 (2019). https://doi.org/10.1007/s10483-019-2450-6

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  • DOI: https://doi.org/10.1007/s10483-019-2450-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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