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基于POD的超声速尾喷焰流场时空降阶模型

孙傲 牛青林 王晓冰

孙傲, 牛青林, 王晓冰. 基于POD的超声速尾喷焰流场时空降阶模型[J]. 航空动力学报, 2024, 39(7):20230419 doi: 10.13224/j.cnki.jasp.20230419
引用本文: 孙傲, 牛青林, 王晓冰. 基于POD的超声速尾喷焰流场时空降阶模型[J]. 航空动力学报, 2024, 39(7):20230419 doi: 10.13224/j.cnki.jasp.20230419
SUN Ao, NIU Qinglin, WANG Xiaobing. Spatiotemporal reduced-order model of supersonic exhaust plume based on proper orthogonal decomposition[J]. Journal of Aerospace Power, 2024, 39(7):20230419 doi: 10.13224/j.cnki.jasp.20230419
Citation: SUN Ao, NIU Qinglin, WANG Xiaobing. Spatiotemporal reduced-order model of supersonic exhaust plume based on proper orthogonal decomposition[J]. Journal of Aerospace Power, 2024, 39(7):20230419 doi: 10.13224/j.cnki.jasp.20230419

基于POD的超声速尾喷焰流场时空降阶模型

doi: 10.13224/j.cnki.jasp.20230419
基金项目: 国家自然科学基金(52006203,U22B2045); 山西省回国留学人员科研资助项目(2021113)
详细信息
    作者简介:

    孙傲(1999-),男,硕士生,主要从事尾喷焰流动及光辐射高效数值计算方法研究。E-mail:sa15536309747@163.com

    通讯作者:

    牛青林(1987-),男,教授,博士,主要从事高速目标流动、传热及光辐射现象学方面的研究。E-mail:niuql@nuc.edu.cn

  • 中图分类号: V435

Spatiotemporal reduced-order model of supersonic exhaust plume based on proper orthogonal decomposition

  • 摘要:

    采用大涡模拟(LES)方法计算三维非定常喷焰流场,采用低通滤波器获得流场的低频、高能量的大尺度相干结构,利用傅里叶变换和本征正交分解(POD)在尾喷焰方位角上进行空间缩减,通过在主导POD时间模态中提取傅里叶模态进行时间缩减,建立超声速尾喷焰湍流的时空降阶模型(ROM)。结果表明:低通滤波器与POD截断均可对尾喷焰的中高频、低能量的小尺度结构实现滤波;前两阶方位角模态占据了射流中80.9%的能量,且主导方位角模态下的压力POD空间模态因压缩波与激波的交互作用在射流核心区出现尖锐峰值现象;尾喷焰温度和组分的POD空间模态因复燃效应的发生在下游呈现出剧烈扰动,第2阶方位角模态的POD空间模态呈现出交替的波包结构,且具有稳定的波长;尾喷焰温度与组分的POD空间模态呈现出相似的波包结构;基于傅里叶模态能量选择的时间缩减方法不仅可以降低数值不稳定性而且重建精度高。该研究可为超声速尾喷焰流场演化规律和特征提取提供理论方法,也可为目标智能化特征工程应用提供支撑。

     

  • 图 1  时空降阶模型分析框架

    Figure 1.  Spatiotemporal reduced-order model analysis framework

    图 2  计算域与网格分布示意图

    Figure 2.  Schematic diagram of computational domain and grid distribution

    图 3  瞬态流场云图(z-x截面)

    Figure 3.  Instantaneous flow field contours (z-x cross sections)

    图 4  低通滤波下的POD模态能量分布

    Figure 4.  POD mode energy distribution under low-pass filtering

    图 5  低通滤波下的方位角模态能量分布

    Figure 5.  Azimuthal mode energy distribution under low-pass filtering

    图 6  m=0第1、5、10阶时间模态的实部分量

    Figure 6.  Real component of the 1st、5th and 10th chronos for the m=0 mode

    图 7  m=0第1、5、10阶时间模态的功率谱密度

    Figure 7.  Power spectral density of the 1st、5th and 10th chronos of for the m=0 mode

    图 8  3个主导方位角模态m=0的空间模态云图

    Figure 8.  Contours of the 3 leading m=0 azimuthal mode topos

    图 9  3个主导方位角模态m=1的空间模态云图

    Figure 9.  Contours of the 3 leading m=1 azimuthal mode topos

    图 10  Ritz特征值分布

    Figure 10.  Ritz eigenvalue distribution

    图 11  原始、重构时间模态(m=1)

    Figure 11.  Ritz eigenvalue distribution (m=1)

    图 12  tROM的重构误差随傅里叶模态数的关系

    Figure 12.  Reconstruction error of tROM as a function of the number of Fourier modes

    图 13  N=F=50时前M个方位角模态总和的能量误差

    Figure 13.  Energy error of the sum of the first M azimuthal modes when N=F=50

    图 14  原始流场、重建流场以及误差流场的压力和温度分布

    Figure 14.  Pressure and temperature distributions of the original flow field, reconstructed flow field, and error flow field

    表  1  发动机喷口流场参数

    Table  1.   Flow parameters of nozzle exit

    H2O CO2 CO N2 H2 OH HCl
    0.4 0.136 0.115 0.1 0.06 0.05 0.19
    下载: 导出CSV

    表  2  时空缩减误差对比

    Table  2.   Comparison of errors in spatio-temporal reduction

    模态截断
    占比K/Kall
    本文重构
    误差/%
    参考文献
    重构误差/%
    1/3 1.5 20.0
    1/30 9.3 30.0
    1/220 22.0 60.0
    下载: 导出CSV
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  • 收稿日期:  2023-06-26
  • 网络出版日期:  2024-03-05

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