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

doi:10.1007/s10483-016-2114-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (8): 1013-1030.doi: https://doi.org/10.1007/s10483-016-2114-8

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

Jianxin LIU¹, Shaolong ZHANG¹, Song FU²

1. Department of Mechanism, Tianjin University, Tianjin 300072, China;
2. School of Aerospace Engineering, Tsinghua University, Beijing 100181, China

Received:2015-10-20 Revised:2016-03-14 Online:2016-08-01 Published:2016-08-01
Contact: Song FU E-mail:fs-dem@tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11272183, 11572176, 11402167, 11202147, and 11332007) and the National Program on Key Basic Research Project of China (No. 2014CB744801)

Abstract

Abstract:

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 (3DLPSE) 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.

Key words: three-dimensional (3D) boundary layer, biglobal instability, three-dimensional linear parabolized stability equation (3D-LPSE), crossflow vortex, Gö, rtler flow

2010 MSC Number:

Jianxin LIU, Shaolong ZHANG, Song FU. Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1013-1030.

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

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