Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

doi:10.1007/s10483-016-2125-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1219-1230.doi: https://doi.org/10.1007/s10483-016-2125-6

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

Shaolong ZHANG, Jianxin LIU, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

收稿日期:2015-12-04 修回日期:2016-03-01 出版日期:2016-09-01 发布日期:2016-09-01
通讯作者: Shaolong ZHANG E-mail:shookware@tju.edu.cn
基金资助:
Project supported by the State Key Program of National Natural Science Foundation of China (No. 11332007) and the Young Scientists Fund of the National Natural Science Foundation of China (No. 11402167)

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

Shaolong ZHANG, Jianxin LIU, Jisheng LUO

Department of Mechanics, Tianjin University, Tianjin 300072, China

Received:2015-12-04 Revised:2016-03-01 Online:2016-09-01 Published:2016-09-01
Contact: Shaolong ZHANG E-mail:shookware@tju.edu.cn
Supported by:
Project supported by the State Key Program of National Natural Science Foundation of China (No. 11332007) and the Young Scientists Fund of the National Natural Science Foundation of China (No. 11402167)

摘要/Abstract

摘要：

The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wallcooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1-1/Ma or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.

关键词: stability, Mack mode instability, wall-cooling, high speed boundary layer

Abstract:

Key words: wall-cooling, stability, high speed boundary layer, Mack mode instability

中图分类号:

76E19
76K05

Shaolong ZHANG, Jianxin LIU, Jisheng LUO. Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1219-1230.

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Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

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