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带冷却气流的亥姆霍兹共振器的声类比模型

甘振鹏 杨东

甘振鹏, 杨东. 带冷却气流的亥姆霍兹共振器的声类比模型. 力学学报, 2022, 54(3): 577-587 doi: 10.6052/0459-1879-21-561
引用本文: 甘振鹏, 杨东. 带冷却气流的亥姆霍兹共振器的声类比模型. 力学学报, 2022, 54(3): 577-587 doi: 10.6052/0459-1879-21-561
Gan Zhenpeng, Yang Dong. An acoustic analogy model for Helmholtz resonators with cooling bias flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 577-587 doi: 10.6052/0459-1879-21-561
Citation: Gan Zhenpeng, Yang Dong. An acoustic analogy model for Helmholtz resonators with cooling bias flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 577-587 doi: 10.6052/0459-1879-21-561

带冷却气流的亥姆霍兹共振器的声类比模型

doi: 10.6052/0459-1879-21-561
基金项目: 南方科技大学科研启动经费资助
详细信息
    作者简介:

    杨东, 助理教授, 主要研究方向: 燃烧热声振荡. E-mail: yangd3@sustech.edu.cn

  • 中图分类号: V231

AN ACOUSTIC ANALOGY MODEL FOR HELMHOLTZ RESONATORS WITH COOLING BIAS FLOW

  • 摘要: 亥姆霍兹共振器(HR)作为典型的被动消声装置, 常被安装于航空发动机和燃气轮机的燃烧室上用以吸收噪声进而抑制燃烧热声振荡. 在实际应用中, 为防止燃烧室内高温气体损坏HR, 常引入冷却气流从HR的背部空腔通过其颈部流入燃烧室, 以保护HR. 该冷却气流的温度一般显著低于燃烧室内的燃气温度. 将这样的HR安装到燃烧室上时, 该温差可能影响燃烧室中HR上、下游的声波与熵波关系, 并进而影响HR的吸声性能. 然而, 在以往研究HR对燃烧室内热声振荡的影响的模型中, 该温差的影响一般被忽略. 本文基于声类比的思想, 建立了一个可预测当带有冷却气流的HR被安装于一个一维声学管道中时的消声性能的理论模型. 该模型基于一维质量、动量和能量守恒方程, 在无黏性耗散作用, 忽略体积力、所有的外来热源和热扩散的假设下, 首次推导出了侧壁安装有带冷却气流的亥姆霍兹共振器的一维燃烧室中的带源项的波动方程. 该方程右侧的源项能体现出共振器对燃烧室内一维声场的影响, 通过该方程可以看到共振器所带来的声源/声耗散是由熵扰动与质量扰动项组成. 由此可以进一步看出由共振器温差所产生的熵扰动会以声源的形式进入燃烧室内的一维声波方程, 并显著地改变HR在其共振频率附近对燃烧室内声场的影响. 通过与已有的阶跃条件模型对比, 验证了该模型预测HR温差对管道内声场的影响的准确性.

     

  • 图  1  安装有亥姆霍兹共振器的一维燃烧室管道

    Figure  1.  A Helmholtz resonator installed in an combustor duct

    图  2  无限薄的积分控制体

    Figure  2.  Infinitely thin integral control body

    3  HR温度1000 K时, 3个模型的压力扰动强度幅值、温度扰动和声吸收系数

    3.  The amplitude of pressure wave strength, temperature oscillationt and absorption coefficien of the three models with a HR temperature of 1000 K

    4  3个模型的压力扰动强度幅值、熵波扰动强度幅值、温度扰动和声吸收系数

    4.  The amplitude of pressure wave strength, enthalpy wave strength, absorption coefficient and temperature oscillation of the three models

    表  1  HR和燃烧室的几何与平均流参数

    Table  1.   Geometry and mean flow parameters of the HR and combustor

    ParameterValue
    HRneck length L/m0.005
    neck sectional area $ {A_n}/{{\rm{m}}^2} $ 0.0001
    mean cavity temperature $ {\bar T_n}/{\rm{K}} $ 500 ~ 1000
    cavity volume $ V/{{\rm{m}}^3} $ 0.00025
    neck mean Mach number $ {\bar M_n} $ 0.01
    combustorupstream mean flow pressure $ {\bar p_1}/{\rm{MPa}} $ 2
    pipe cross-sectional area $ {A_c}/{{\rm{m}}^2} $ 0.01π
    upstream mean flow temperature ${\bar T_1}/{\rm{K}}$ 1000
    upstream mean Mach number $ {\bar M_1} $ 0.03
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-31
  • 录用日期:  2022-02-19
  • 网络出版日期:  2022-02-20
  • 刊出日期:  2022-03-18

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