中国物理B ›› 2015, Vol. 24 ›› Issue (12): 124701-124701.doi: 10.1088/1674-1056/24/12/124701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Application of Arnoldi method to boundary layer instability

张永明a b, 罗纪生a   

  1. a Department of Mechanics, Tianjin University, Tianjin 300072, China;
    b Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin 300072, China
  • 收稿日期:2015-05-29 修回日期:2015-07-20 出版日期:2015-12-05 发布日期:2015-12-05
  • 通讯作者: Zhang Yong-Ming E-mail:ymzh@tju.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).

Application of Arnoldi method to boundary layer instability

Zhang Yong-Ming (张永明)a b, Luo Ji-Sheng (罗纪生)a   

  1. a Department of Mechanics, Tianjin University, Tianjin 300072, China;
    b Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin 300072, China
  • Received:2015-05-29 Revised:2015-07-20 Online:2015-12-05 Published:2015-12-05
  • Contact: Zhang Yong-Ming E-mail:ymzh@tju.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).

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摘要：

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘angerous' in secondary instability.

关键词: Arnildi method, linear stability theory, Floquet theory, secondary instability

Abstract:

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘angerous' in secondary instability.

Key words: Arnildi method, linear stability theory, Floquet theory, secondary instability

中图分类号:  (Instability of boundary layers; separation)

  • 47.20.Ib
47.20.Lz (Secondary instabilities)