基于调和线性化Navier-Stokes方程的局部感受性

黄加昊; 赵磊; 赵瑞

doi:10.7638/kqdlxxb-2023.0068

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基于调和线性化Navier-Stokes方程的局部感受性

研究论文 | 更新时间：2026-05-28

- 基于调和线性化Navier-Stokes方程的局部感受性
- Local receptivity based on harmonic linearized Navier-Stokes equations
- 空气动力学学报 2024年42卷第3期页码：69-82
- 作者机构：
  
  1. 天津大学力学系,天津,300350
  2. 天津市现代工程力学重点实验室,天津,300350
  3. 北京理工大学宇航学院,北京,100081
- 作者简介：
  
  黄加昊（1998—），男，浙江人，研究方向：边界层流动稳定性. E-mail：hjh1998@tju.edu.cn
  赵磊*，副教授，研究方向：流动稳定性与边界层转捩. E-mail：lei_zhao@tju.edu.cn
- 基金信息：
  
  国家自然科学基金青年基金（12002235）;国家自然科学基金企业联合基金重点项目（U20B2003）
- DOI：10.7638/kqdlxxb-2023.0068
  中图分类号： V211;V411
- 纸质出版：2024
- 稿件说明：
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黄加昊, 赵磊, 赵瑞. 基于调和线性化Navier-Stokes方程的局部感受性[J]. 空气动力学学报, 2024, 42(3): 69−82.

HUANG Jiahao, ZHAO Lei, ZHAO Rui. Local receptivity based on harmonic linearized Navier-Stokes equations[J]. 2024, 42(3): 69-82.
黄加昊, 赵磊, 赵瑞. 基于调和线性化Navier-Stokes方程的局部感受性[J]. 空气动力学学报, 2024, 42(3): 69−82. DOI： 10.7638/kqdlxxb-2023.0068

HUANG Jiahao, ZHAO Lei, ZHAO Rui. Local receptivity based on harmonic linearized Navier-Stokes equations[J]. 2024, 42(3): 69-82. DOI： 10.7638/kqdlxxb-2023.0068.

摘要

高超声速边界层中Mack模态的感受性决定了触发转捩的扰动的初始幅值，因而考虑感受性是构建合理的转捩预测方法的前提。壁面粗糙元与来流声波作用从而激发Mack模态是典型的局部感受性过程，对该过程的描述方法大致包括大雷诺数渐近理论、有限雷诺数理论和直接数值模拟。由于需要做小粗糙元线性假设，所以前两种方法无法有效预测有限高度粗糙元工况，而第三种方法则由于计算量庞大而无法进行参数化研究。本文发展了一套基于调和线性化Navier-Stokes方程的局部感受性高效算法，并针对马赫数5.92的高超声速平板边界层系统地研究了小尺度及有限高度粗糙元与声波引起的Mack模态感受性。结果表明，快声波诱导Mack模态的局部感受性显著强于慢声波。对于有限高度粗糙元，快声波的局部感受性在较大声波参数范围内随粗糙元高度增加而超线性增强。

Abstract

The receptivity of Mack mode in the hypersonic boundary layer determines the initial amplitudes of disturbances that trigger transition. Therefore

considering the receptivity is a fundamental prerequisite for developing rational transition prediction methods. The excitation of Mack mode by the interaction between localized wall roughness and incoming acoustic waves is a typical local receptivity process

which can be generally described by three methods

i.e.

the large-Reynolds-number asymptotic theory

the finite-Reynolds-number theory

and direct numerical simulations. However

the first two theories become invalid under the condition of finite-height roughness due to the hypothesis of small (linear) roughness involved

whereas the third method is computationally intensive and not suitable for parametric study. In the present study

an efficient method for computing the local receptivity is developed based on the harmonic linearized Navier-Stokes equation (HLNS)

and the local receptivity of Mack mode

induced by the interaction between the acoustic wave and the small/finite-height roughness

is systematically investigated in the hypersonic boundary layer at a Mach number of 5.92. The results suggest that the local receptivity of Mack mode induced by fast acoustic waves is significantly stronger than that of slow acoustic waves. For finite-height roughness

the local receptivity of fast acoustic waves shows a super-linear enhancement with the increase of roughness height within a large range of acoustic parameters.

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Keywords

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