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基于HLNS方法对高超声速边界层中非模态扰动演化的研究

孙培成 赵磊 董明

孙培成, 赵磊, 董明. 基于HLNS方法对高超声速边界层中非模态扰动演化的研究. 力学进展, 2022, 52(1): 180-195 doi: 10.6052/1000-0992-22-003
引用本文: 孙培成, 赵磊, 董明. 基于HLNS方法对高超声速边界层中非模态扰动演化的研究. 力学进展, 2022, 52(1): 180-195 doi: 10.6052/1000-0992-22-003
Sun P C, Zhao L, Dong M. Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach. Advances in Mechanics, 2022, 52(1): 180-195 doi: 10.6052/1000-0992-22-003
Citation: Sun P C, Zhao L, Dong M. Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach. Advances in Mechanics, 2022, 52(1): 180-195 doi: 10.6052/1000-0992-22-003

基于HLNS方法对高超声速边界层中非模态扰动演化的研究

doi: 10.6052/1000-0992-22-003
基金项目: 本文受到国家自然科学基金的资助(12002235, U20B2003).
详细信息
    作者简介:

    赵磊, 天津大学机械工程学院助理教授, 硕士生导师. 主要研究领域为流动稳定性、边界层转捩等. 获国家自然科学基金青年基金资助, 参与国家自然科学基金重点基金1项

    通讯作者:

    lei_zhao@tju.edu.cn

  • 中图分类号: O357.4+1

Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach

More Information
  • 摘要: 高超声速边界层转捩是航天飞行器设计中的基础难题, 发生在线性失稳区上游的亚临界转捩是常规风洞实验中常见的现象. 亚临界转捩一般是由非模态扰动的演化及二次失稳触发的, 为了揭示局部突变对高超声速边界层亚临界转捩的影响机理, 发展了基于谐波型线性化Navier-Stokes (HLNS) 方程及其伴随系统的描述非模态扰动演化的求解框架. 该框架的优点是不改变原始系统的椭圆型特性, 因而可以处理非模态扰动 (条带) 在局部突变附近的快速畸变. 针对马赫数为5.96、攻角为$ - 4^\circ $的高超声速钝平板边界层, 研究了不同深度凹槽对条带幅值的影响. 数值结果表明凹槽对条带有促进作用, 这与实验中发现的规律定性相符, 且存在使促进作用最大的最优凹槽深度.

     

  • 图  1  物理模型示意图

    图  2  凹槽附近的网格示意图

    图  3  平均流压力等值线图. (a) H = 0.1, (b) H = 0.15, (c) H = 0.2, (d) H = 0.4

    图  4  不同深度凹槽下壁面速度剪切率(a)以及壁面压力(b)的流向分布

    图  5  凹槽内流向速度等值线图及流线图. (a) H = 0.1, (b) H = 0.15, (c) H = 0.2, (d) H = 0.4

    图  6  固定入口(a)、出口(b)时不同计算域下最优能量增益随展向波数的变化

    图  7  最优扰动在入口(a)、出口(b)处的特征函数剖面($ \beta = 2.8 $)

    图  8  (a) HLNS与DNS计算的幅值Au对比, (b)及流向速度扰动的空间结构($ \beta = 2.8 $)

    图  9  (a)不同深度凹槽下的最优能量增益随展向波数的变化, (b)最优能量增益随凹槽深度的变化

    图  10  (a) HLNS与DNS计算的凹槽作用下的幅值Au对比, (b)及流向速度扰动的空间结构(H = 0.2, $ \beta = 2.8 $)

    图  11  不同深度凹槽下的最优扰动的能量$ E(x) $(a)以及归一化能量$ \bar E(x) $(b)沿流向的演化

    图  12  放大因子$T$随着凹槽深度H的分布($ \beta = 2.8 $)

    A1  不同网格数下的速度(a)、密度(b)剖面对比

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出版历程
  • 收稿日期:  2022-01-13
  • 录用日期:  2022-02-24
  • 网络出版日期:  2022-03-04
  • 刊出日期:  2022-03-25

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