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

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

孙傲^1,,
牛青林^1,*, ,,
王晓冰²

1.
中北大学机电工程学院，太原 030051
2.
上海无线电设备研究所电磁散射重点实验室，上海 200438

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
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出版历程
- 收稿日期: 2023-06-26
- 网络出版日期: 2024-03-05

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

SUN Ao^1
,,
NIU Qinglin^{1,*
, ,},
WANG Xiaobing²

1.
School of Mechanical and Electrical Engineering，North University of China，Taiyuan 030051，China
2.
Science and Technology on Electromagnetic Scattering Laboratory，Shanghai Radio Equipment Research Institute，Shanghai 200438，China

摘要

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。
- 尾喷焰 /
- 时空降阶模型 /
- 本征正交分解 /
- 相干结构 /
- 时空模态
Abstract:
Large Eddy Simulation (LES) was used to compute the three-dimensional unsteady plume flow field. Low-frequency and high-energy large-scale coherent structures in the flow field were extracted by using low-pass filters. Spatial reduction was achieved by Fourier transform and Proper Orthogonal Decomposition (POD) in the azimuthal direction of the plume, while temporal reduction was achieved by extracting the Fourier mode from the leading temporal POD mode. Consequently, a spatiotemporal reduced-order model (ROM) for supersonic plume reaction turbulence was established. The results demonstrated that low-pass filters and POD truncation can successfully filter high-frequency and low-energy small-scale structures in the supersonic plume. The azimuthal modes m=0 and m=1 accounted for 80.9% of the energy in the plume. In the m=0 azimuthal mode, the pressure POD spatial mode showed sharp peaks in the core region of the jet due to the interaction between compression wave and shock wave. Furthermore, POD spatial modes of the component and temperature exhibited sharp disturbances downstream because of afterburning. An alternating wave packet structure with a steady wavelength was displayed in the POD spatial mode under the m=1 azimuthal mode. The POD spatial mode of both components and temperature showed a similar wave packet structure. In addition to reducing numerical instability, temporal reduction based on Fourier mode energy selection guaranteed excellent reconstruction accuracy. This research can support target intelligent feature engineering applications by offering theoretical techniques for evolution laws and feature extraction on supersonic rocket exhaust plumes.
- rocket exhaust plume /
- spatiotemporal reduced-order model /
- proper orthogonal decomposition /
- coherent structure /
- spatiotemporal mode

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图 1 时空降阶模型分析框架

Figure 1. Spatiotemporal reduced-order model analysis framework

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图 2 计算域与网格分布示意图

Figure 2. Schematic diagram of computational domain and grid distribution

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图 3 瞬态流场云图（z-x截面）

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

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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

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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

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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

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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

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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

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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

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图 10 Ritz特征值分布

Figure 10. Ritz eigenvalue distribution

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图 11 原始、重构时间模态（m=1）

Figure 11. Ritz eigenvalue distribution （m=1）

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图 12 t_ROM的重构误差随傅里叶模态数的关系

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

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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

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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

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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

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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/K_all 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

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