中国物理B ›› 2016, Vol. 25 ›› Issue (8): 84701-084701.doi: 10.1088/1674-1056/25/8/084701

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

Improved algorithm for solving nonlinear parabolized stability equations

Lei Zhao(赵磊), Cun-bo Zhang(张存波), Jian-xin Liu(刘建新), Ji-sheng Luo(罗纪生)   

  1. Department of Mechanics, Tianjin University, Tianjin 300072, China
  • 收稿日期:2016-01-29 修回日期:2016-03-28 出版日期:2016-08-05 发布日期:2016-08-05
  • 通讯作者: Jian-xin Liu E-mail:shookware@tju.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

Improved algorithm for solving nonlinear parabolized stability equations

Lei Zhao(赵磊), Cun-bo Zhang(张存波), Jian-xin Liu(刘建新), Ji-sheng Luo(罗纪生)   

  1. Department of Mechanics, Tianjin University, Tianjin 300072, China
  • Received:2016-01-29 Revised:2016-03-28 Online:2016-08-05 Published:2016-08-05
  • Contact: Jian-xin Liu E-mail:shookware@tju.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

摘要: Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers.

关键词: improved NPSE approach, stationary crossflow vortices, fundamental resonance, hypersonic boundary layers

Abstract: Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers.

Key words: improved NPSE approach, stationary crossflow vortices, fundamental resonance, hypersonic boundary layers

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

  • 47.20.Ib
47.40.Ki (Supersonic and hypersonic flows) 47.20.Lz (Secondary instabilities)