Stability analysis method considering non-parallelism:EPSE method and its application

doi:10.1007/s10483-016-2013-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (1): 27-36.doi: https://doi.org/10.1007/s10483-016-2013-9

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Stability analysis method considering non-parallelism:EPSE method and its application

Gaotong YU, Jun GAO, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

Received:2015-03-20 Revised:2015-04-27 Online:2016-01-01 Published:2016-01-01
Contact: Jisheng LUO E-mail:jsluo@tju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11332007, 11172203, and 91216111)

Abstract

Abstract:

The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory (LST) based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation (PSE) method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation (DNS). In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.

Key words: linear stability theory (LST), expansion of PSE (EPSE), non-parallel, parabolized stability equation (PSE), normalized method

2010 MSC Number:

76N99

Gaotong YU, Jun GAO, Jisheng LUO. Stability analysis method considering non-parallelism:EPSE method and its application. Applied Mathematics and Mechanics (English Edition), 2016, 37(1): 27-36.

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Stability analysis method considering non-parallelism:EPSE method and its application

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