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Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

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Abstract

An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the eN transition prediction in general three-dimensional boundary layers.

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Acknowledgements

The authors would like to thank Xuezhi LU and Zhenrong JING for valuable discussion and for providing some of the DNS data.

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Authors and Affiliations

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

    Yufeng Han, Jianxin Liu & Jisheng Luo

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

    Jianxin Liu

Authors
  1. Yufeng Han
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  2. Jianxin Liu
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  3. Jisheng Luo
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Corresponding author

Correspondence to Jianxin Liu.

Additional information

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

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Han, Y., Liu, J. & Luo, J. Improvement for expansion of parabolized stability equation method in boundary layer stability analysis. Appl. Math. Mech.-Engl. Ed. 39, 1737–1754 (2018). https://doi.org/10.1007/s10483-019-2401-9

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  • DOI: https://doi.org/10.1007/s10483-019-2401-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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