Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

doi:10.1007/s10483-017-2227-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (8): 1109-1126.doi: https://doi.org/10.1007/s10483-017-2227-9

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Cunbo ZHANG, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

收稿日期:2016-12-27 修回日期:2017-03-23 出版日期:2017-08-01 发布日期:2017-08-01
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)

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Cunbo ZHANG, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

Received:2016-12-27 Revised:2017-03-23 Online:2017-08-01 Published:2017-08-01
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：

Nonlinear interactions of the two-dimensional (2D) second mode with oblique modes are studied numerically in a Mach 6.0 flat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation (PSE) method, which is able to simulate interaction of two modes with different frequencies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

关键词: multivariable spline element method, bicubic B spline, plate on elastic foundation, nonlinear mode interaction, supersonic boundary layer, boundary layer instability

Abstract:

Key words: multivariable spline element method, bicubic B spline, plate on elastic foundation, boundary layer instability, nonlinear mode interaction, supersonic boundary layer

中图分类号:

Cunbo ZHANG, Jisheng LUO. Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1109-1126.

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Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

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