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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

  • [1] 董明. 2020. 边界层转捩预测中的局部散射理论. 空气动力学学报, 38: 286-298 (Dong M. 2020. Local scattering theory for transition prediction in boundary-layer flows. Acta Aerodynamica Sinica, 38: 286-298).
    [2] 李强, 赵磊, 陈苏宇, 江涛, 庄宇, 张扣立. 2020. 展向凹槽及泄流孔对高超声速平板边界层转捩影响的试验研究. 物理学报, 69: 024703 (Li Q, Zhao L, Chen S Y, Jiang T, Zhuang Y, Zhang K L. 2020. Experimental study on effect of transverse groove with/without discharge hole on hypersonic blunt flat-plate boundary layer transition. Acta Phys Sin, 69: 024703). doi: 10.7498/aps.69.20191155
    [3] 李斯特, 董明. 2021. 局部散射理论在高超声速边界层转捩预测中应用的检验. 力学进展, 51: 364-375 (Li S T, Dong M. 2021. Verification of local scattering theory as is applied to transition prediction in hypersonic boundary layers. Advances in Mechanics, 51: 364-375). doi: 10.6052/1000-0992-21-016
    [4] 赵磊. 2017. 高超声速后掠钝板边界层横流定常涡失稳的研究. [博士论文]. 天津: 天津大学

    Zhao L. 2017. Study on instability of stationary crossflow vortices in hypersonic swept blunt plate boundary layers. [PhD Thesis]. Tianjin: Tianjin University
    [5] Dong M, Li C. 2021. Effect of two-dimensional short rectangular indentations on hypersonic boundary-layer transition. AIAA Journal, 59: 7 DOI: 10.2514/1.J059957.
    [6] Dong M, Liu Y H, Wu X S. 2020. Receptivity of inviscid modes in supersonic boundary layers due to scattering of free-stream sound by localised wall roughness. Journal of Fluid Mechanics, 896: A23. doi: 10.1017/jfm.2020.358
    [7] Dong M, Zhao L. 2021. An asymptotic theory of the roughness impact on inviscid Mack modes in supersonic/hypersonic boundary layers. Journal of Fluid Mechanics, 913: A22. doi: 10.1017/jfm.2020.1146
    [8] Henningson D. 1995. Bypass transition and linear growth mechanisms. Advances in Turbulence V. Springer, 1: 190-204.
    [9] Leib S J, Wundrow D W, Goldstein M E. 1999. Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. Journal of Fluid Mechanics, 380: 169-203. doi: 10.1017/S0022112098003504
    [10] Liu Y H, Dong M, Wu X S. 2020. Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness. Journal of Fluid Mechanics, 888: A10. doi: 10.1017/jfm.2020.38
    [11] Luchini P. 2000. Reynolds-number-independent instability of the boundary layer over a flat surface optimal perturbations. Journal of Fluid Mechanics, 404: 289-309. doi: 10.1017/S0022112099007259
    [12] Paredes P, Choudhari M M, Li F, et al. 2016. Optimal growth in hypersonic boundary layers. AIAA Journal, 54: 3050-3061. doi: 10.2514/1.J054912
    [13] Paredes P, Choudhari M M, Li F. 2017. Blunt-body paradox and transient growth on a hypersonic spherical forebody. Physical Review Fluids, 2: 053903. doi: 10.1103/PhysRevFluids.2.053903
    [14] Paredes P, Choudhari M M, Li F, et al. 2018. Nose-tip bluntness effects on transition at hypersonic speeds. Journal of Spacecraft and Rockets, 56: 1-19. doi: 10.2514/1.A34277
    [15] Ricco P, Luo J S, Wu X S. 2011. Evolution and instability of unsteady nonlinear streaks generated by free-stream vortical disturbances. Journal of Fluid Mechanics, 677: 1-38. doi: 10.1017/jfm.2011.41
    [16] Song R, Zhao L, Huang Z. F. 2020. Improvement of the parabolized stability equation to predict the linear evolution of disturbances in three-dimensional boundary layers based on ray tracing theory. Physical Review Fluids, 5: . doi: 10.1103/PhysRevFluids.5.033901
    [17] Tempelmann D, Hanifi A, Henningson D S. 2010. Spatial optimal growth in three-dimensional boundary layers. Journal of Fluid Mechanics, 646: 5-37. doi: 10.1017/S0022112009993260
    [18] Tempelmann D, Hanifi A, Henningson D S. 2012. Spatial optimal growth in three-dimensional compressible boundary layers. Journal of Fluid Mechanics, 704: 251-279. doi: 10.1017/jfm.2012.235
    [19] Trefethen L N, Trefethen A E, Reddy S C, et al. 1993. Hydrodynamic stability without eigenvalues. Science, 261: 578-584. doi: 10.1126/science.261.5121.578
    [20] Tumin A, Reshotko E. 2001. Spatial theory of optimal disturbances in boundary layers. Physics of Fluids, 13: 2097-2104. doi: 10.1063/1.1378070
    [21] Wu X S, Dong M. 2016. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794: 68-108. doi: 10.1017/jfm.2016.125
    [22] Zhang A Y, Dong M, Zhang Y M. 2018. Receptivity of secondary instability modes in streaky boundary layers. Physics of Fluids, 30: 114102. doi: 10.1063/1.5046136
    [23] Zhao L, Zhang C B, Liu J X, Luo J S. 2016. Improved algorithm for solving nonlinear parabolized stability equations. Chinese Physics B, 25: 084701. doi: 10.1088/1674-1056/25/8/084701
    [24] Zhao L, Dong M, Yang Y G. 2019. Harmonic linearized Navier-Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition. Physics of Fluids, 31: 034108. doi: 10.1063/1.5086912
    [25] Zhao L, Dong M. 2020. Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps. Physics of Fluids, 32: 054108. doi: 10.1063/5.0007624
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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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