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Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (7): 835-846.doi: https://doi.org/10.1007/s10483-015-1951-9

• •    下一篇

Self-consistent parabolized stability equation (PSE) method for compressible boundary layer

Yongming ZHANG1,2, Caihong SU1,2   

  1. 1. Department of Mechanics, Tianjin University, Tianjin 300072, China;
    2. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin University, Tianjin 300072, China
  • 收稿日期:2014-06-12 修回日期:2014-11-16 出版日期:2015-07-01 发布日期:2015-07-01
  • 通讯作者: Yongming ZHANG E-mail:ymzh@tju.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Nos. 11202147, 11472188, 11332007, 11172203, and 91216111) and the Specialized Research Fund (New Teacher Class) for the Doctoral Program of Higher Education (No. 20120032120007)

Self-consistent parabolized stability equation (PSE) method for compressible boundary layer

Yongming ZHANG1,2, Caihong SU1,2   

  1. 1. Department of Mechanics, Tianjin University, Tianjin 300072, China;
    2. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin University, Tianjin 300072, China
  • Received:2014-06-12 Revised:2014-11-16 Online:2015-07-01 Published:2015-07-01
  • Contact: Yongming ZHANG E-mail:ymzh@tju.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Nos. 11202147, 11472188, 11332007, 11172203, and 91216111) and the Specialized Research Fund (New Teacher Class) for the Doctoral Program of Higher Education (No. 20120032120007)

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摘要： The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.

关键词: parabolized stability equation (PSE), boundary layer, self-consistent, direct numerical simulation (DNS)

Abstract: The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.

Key words: self-consistent, boundary layer, direct numerical simulation (DNS), parabolized stability equation (PSE)

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