超声速边界层中的模态转换及壁温影响效应

苏彩虹; 宋明真

doi:10.7638/kqdlxxb-2019.0048

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超声速边界层中的模态转换及壁温影响效应

研究论文 | 更新时间：2026-05-28

- 超声速边界层中的模态转换及壁温影响效应
- Intermodal exchange and wall temperature effect in a supersonic boundary layer
- 空气动力学学报 2020年38卷第6期页码：1056-1063
- 作者机构：
  
  天津大学机械学院高速空气动力学研究室,天津,300072
- 作者简介：
  
  苏彩虹(1979-), 女, 内蒙古自治区包头市人, 教授, 研究方向:稳定性分析和转捩预测.E-mail:su_ch@tju.edu.cn
- 基金信息：
- DOI：10.7638/kqdlxxb-2019.0048
  中图分类号： O357.4
- 纸质出版：2020
- 稿件说明：
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苏彩虹, 宋明真. 超声速边界层中的模态转换及壁温影响效应[J]. 空气动力学学报, 2020, 38(6): 1056-1063.

SU Caihong, SONG Mingzhen. Intermodal exchange and wall temperature effect in a supersonic boundary layer[J]. 2020, 38(6): 1056-1063.
苏彩虹, 宋明真. 超声速边界层中的模态转换及壁温影响效应[J]. 空气动力学学报, 2020, 38(6): 1056-1063. DOI： 10.7638/kqdlxxb-2019.0048.

SU Caihong, SONG Mingzhen. Intermodal exchange and wall temperature effect in a supersonic boundary layer[J]. 2020, 38(6): 1056-1063. DOI： 10.7638/kqdlxxb-2019.0048.

摘要

对于马赫数大于4的超声速边界层，Mack第二模态起主导作用。根据感受性的研究，生成第二模态的一个重要途径是，边界层内的快模态在下游演化过程中因相速度“同步”而发生模态转换。采用数值方法研究了超声速平板边界层中快模态到第二模态波的模态转换过程，通过定义模态转换系数和模态转换区间，建立了适用于多个不同壁面温度条件下的模态转换系数和转换区间与扰动频率之间的模型公式。在此基础上，基于线性稳定性理论，发展了包含模态转换过程的扰动演化的计算方法，并采用抛物化稳定性方程进行了验证。结果表明，在较广泛的壁面温度条件下，该方法可以准确计算包含快模态到第二模态转换过程的幅值演化。该方法由于考虑了第二模态的生成机制，比原有的基于线性理论的转捩预测方法更加具有物理依据。

Abstract

At free-stream Mach number larger than 4

the second mode is the dominant instability mode in supersonic boundary layers. According to the findings from receptivity research

one important way to generate the second mode is through intermodal exchange

by which the excited fast mode in the boundary layer synchronizes with the second mode when travels downstream. In this paper

the intermodal exchange between the fast mode and the second mode in a supersonic boundary layer is investigated numerically. Two coefficients

i.e. the amplitude and region of intermodal exchange are defined. Their relations are established with respect to the disturbance frequency. Based on linear stability theory

a new method accounting for the intermodal exchange is developed to compute the evolutions of the disturbances. The parabolized stability equations is used to verify the new method. It is shown that

under a wide range of wall temperature conditions

the newly developed method can accurately predict the evolutions of the disturbance considering the process of intermodal exchange between fast mode and the second mode. With considerations of the initial amplitude of the excited fast mode and a transition criterion

this method can be easily used to predict transition of a boundary layer. Since it considers the generation of the second mode through intermodal exchange

it accounts for more physics than the conventional transition prediction method.

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references

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