Conservation relation of generalized growth rate in boundary layers  

作　　者：Runjie SONG Lei ZHAO Zhangfeng HUANG 

机构地区：[1]Department of Mechanics, Tianjin University [2]Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第12期1755-1768,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11672351 and11332007);the National Key R&D Plan(No.2016YFA0401200);the FengLei Youth Innovation Fund of China Aerodynamics Research and Development Center(No.KT-FLJJ-201803)

摘　　要：The elementary task is to calculate the growth rates of disturbances when the e;method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional（3 D） flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts.The generalized growth rate（GGR） in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the eN method in 3 D flows is discussed, and the puzzle of determining growth rates in 3 D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3 D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90?which can be easily avoided in practical application.The elementary task is to calculate the growth rates of disturbances when the e^N method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional(3 D) flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts.The generalized growth rate(GGR) in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the eN method in 3 D flows is discussed, and the puzzle of determining growth rates in 3 D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3 D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90?which can be easily avoided in practical application.

关 键 词：generalized growth rate(GGR) boundary layer stability e^N method 

分 类 号：O357.4[理学—流体力学] O29[理学—力学]