Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

doi:10.1007/s10483-017-2214-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (7): 981-996.doi: https://doi.org/10.1007/s10483-017-2214-6

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

Xuezhi LU, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

收稿日期:2016-07-01 修回日期:2016-11-18 出版日期:2017-07-01 发布日期:2017-07-01
通讯作者: Jisheng LUO, E-mail:jsluo@tju.edu.cn E-mail:jsluo@tju.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11332007)

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

Xuezhi LU, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

Received:2016-07-01 Revised:2016-11-18 Online:2017-07-01 Published:2017-07-01
Contact: Jisheng LUO E-mail:jsluo@tju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11332007)

摘要/Abstract

摘要：

The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient e^N prediction tool for the crossflow instability in swept-wing boundary-layer flows.

关键词: approximate inertial manifold, weakly damped forced KdV equation, dynamical system, attractor, non-parallelism, swept-wing boundary layer, crossflow instability, expansion of parabolized stability equation (EPSE), e^N prediction tool

Abstract:

Key words: approximate inertial manifold, weakly damped forced KdV equation, dynamical system, attractor, swept-wing boundary layer, crossflow instability, e^N prediction tool, non-parallelism, expansion of parabolized stability equation (EPSE)

中图分类号:

76N99

Xuezhi LU, Jisheng LUO. Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 981-996.

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Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

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