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Extension of e N method to general three-dimensional boundary layers

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Abstract

In order to extend the e N method to general three-dimensional boundary layers, the conservation law of the imaginary parts for the wave parameters with a fixed wave vector is deduced. The compatibility relationship (CR) and the general theory of ray tracing (RT), which have been extensively used in conservative systems, are applied to a general three-dimensional boundary layer belonging to non-conservative systems. Two kinds of e N methods, i.e., the eN-CR method and the eN-RT method, are established. Both the two kinds of methods can be used to predict the evolutions of the spanwise wavenumber and the amplitude of the disturbances in general three-dimensional boundary layers. The reliability of the proposed methods is verified and validated by performing a direct numerical simulation (DNS) in a hypersonic general three-dimensional boundary layer over an aircraft model. The results are also compared with those obtained by other e N methods, indicating that the proposed methods have great potential applications in improving the transition prediction accuracy in general three-dimensional boundary layers.

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Acknowledgements

The authors are grateful to Professor Xuesong WU of Imperial College London for valuable discussion and suggestions.

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Authors and Affiliations

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

    Lei Zhao, Gaotong Yu & Jisheng Luo

  2. The 41st Institute of No. 6 Academy, China Aerospace Science & Industry Corporation, Hohhot, 010010, China

    Gaotong Yu

Authors
  1. Lei Zhao
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  2. Gaotong Yu
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  3. Jisheng Luo
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Corresponding author

Correspondence to Jisheng Luo.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11332007) and the Natural Science Foundation of Tianjin (No. 15JCYBJC19500)

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Zhao, L., Yu, G. & Luo, J. Extension of e N method to general three-dimensional boundary layers. Appl. Math. Mech.-Engl. Ed. 38, 1007–1018 (2017). https://doi.org/10.1007/s10483-017-2215-6

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  • DOI: https://doi.org/10.1007/s10483-017-2215-6

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2010 Mathematics Subject Classification

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