Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE  

作　　者：Jianxin LIU Shaolong ZHANG Song FU 

机构地区：[1]Department of Mechanism,Tianjin University [2]School of Aerospace Engineering,Tsinghua University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第8期1013-1030,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11272183,11572176,11402167,11202147,and 11332007);the National Program on Key Basic Research Project of China(No.2014CB744801)

摘　　要：It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional （3D） boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation （3D- LPSE） approach, a 3D extension of the two-dimensional LPSE （2D-LPSE）, is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation （DNS） rather than a 2D-eigenvalue problem （EVP） procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.

关 键 词：three-dimensional linear parabolized stability equation （3D-LPSE） bi-global instability three-dimensional （3D） boundary layer Gortler fow crossflow vortex 

分 类 号：O357.41[理学—流体力学] O354.4[理学—力学]