Modal diagnostics and nonlinear interaction mechanisms of supersonic jets based on TBOS
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摘要:
针对高马赫数喷流中主导扰动结构难以识别、声源远场辐射机制模糊与非线性交互路径缺乏量化等问题，提出了一种融合了层析重建技术的背景定向纹影（TBOS）实验、密度-压力层析反演、POD模态分解、复模态构建与非线性交互张量分析的多物理场模态识别框架。该方法以马赫数为1.26与1.53两种典型啸音工况为例，通过TBOS技术层析重建轴对称流场密度与压力结构，揭示剪切层与激波的耦合演化过程。构建复模态场并量化主导波长，发现高马赫数下，主导波长增大17%，明确表征剪切层-激波驱动下声波远场辐射结构的有序化。POD频谱主频与理论模型吻合度达99.7%，验证声反馈路径的存在。此外，还引入了Hilbert变换与三模态能量转移张量，发现主模态锁频结构由1-2协同转向1-3强耦合，反馈路径由集中单通道向多模态并联扩散演化，揭示了高马赫喷流中主导模态体系重构与多尺度能量协同调制机制。研究利用单相机投影，结合TBOS可视化技术，建立了“结构识别-传播提取-非线性交互”三层耦合路径，一定程度上突破了传统POD难以辨析主瓣声源演化的瓶颈，为啸音控制、喷流调制与远场辐射建模提供了一种范式与技术支撑。
Abstract:To address the challenges of unclear identification of dominant disturbance structures, ambiguous far-field radiation mechanisms of sound sources, and the lack of quantification for nonlinear interaction paths in high-Mach-number jet flows, a multiphysics modal identification framework integrating tomography-integrated Background-Oriented Schlieren (TBOS) experiments, density-pressure tomographic inversion, Proper Orthogonal Decomposition (POD), complex mode construction, and nonlinear interaction tensor analysis was proposed. Taking Mach number of 1.26 and 1.53 screeching jet conditions as typical cases, the framework tomographically reconstructed the axisymmetric flow field’s density and pressure structures via TBOS, revealing the coupling evolution process between shear layers and shock cells. By constructing the complex mode fields and quantifying the dominant wavelength, it was found that at higher Mach numbers, the dominant wavelength increased by 17%, which explicitly characterized the ordering of far-field acoustic radiation structures induced by shear-shock coupling. The dominant frequencies extracted from POD spectra matched theoretical models with 99.7% accuracy, validating the existence of acoustic feedback paths. Furthermore, Hilbert transform and triadic modal energy transfer tensors revealed that as the Mach number increased, the phase-locking structure of dominant modes transitted from Mode 1-2 coordination to strong Mode 1-3 coupling, accompanied by a shift in energy transport from concentrated single-path feedback to multi-modal distributed interaction. This revealed the reconstruction of dominant modal systems and multi-scale energy cooperative modulation mechanisms in high-Mach-number jets. Utilizing single-camera projection combined with TBOS visualization technology, a three-layer coupling path “structural identification-propagation extraction-nonlinear interaction analysis” was establishes which overcame the limitation of conventional POD to some extent in resolving the evolution of main-lobe acoustic sources. This framework can provide a paradigm and technical support for screech mode identification, jet modulation, and far-field acoustic modeling in supersonic flows.
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图 2 图像互相关位移提取原理
Figure 2. Principle of displacement extraction via image cross-correlation
图 4 背景定向纹影测试装置
Figure 4. Experimental setup for background-oriented schlie-ren measurement
图 6 Ma=1.26工况的X方向瞬时位移场
Figure 6. Instantaneous X-directional displacement field at Ma=1.26
图 7 Ma=1.26工况的X向时均位移场
Figure 7. Time-averaged X-directional displacement field at Ma=1.26
图 8 Ma=1.26工况下的Y方向瞬时位移场
Figure 8. Instantaneous Y-directional displacement field at Ma=1.26
图 9 Ma=1.26工况下的Y方向时均位移场
Figure 9. Time-averaged Y-directional displacement field at Ma=1.26
图 10 Ma=1.53工况的X方向瞬时位移场
Figure 10. Instantaneous X-directional displacement field at Ma=1.53
图 11 Ma=1.53工况的X方向时均位移场
Figure 11. Time-averaged X-directional displacement field at Ma=1.53
图 12 Ma=1.53工况的Y方向瞬时位移场
Figure 12. Instantaneous Y-directional displacement field at Ma=1.53
图 13 Ma=1.53工况的Y方向时均位移场
Figure 13. Time-averaged Y-directional displacement field at Ma=1.53
图 14 Ma=1.26喷流密度场的层析重建结果
Figure 14. Tomographic reconstruction of the density field in jet flow at Ma=1.26
图 16 Ma=1.53喷流密度场的层析重建结果
Figure 16. Tomographic reconstruction of the density field in Jet Flow at Ma=1.53
图 20 Ma=1.26前6阶模态空间分布特征
Figure 20. Spatial distribution of the first six POD modes at Ma=1.26
图 21 Ma=1.53前6阶模态空间分布特征
Figure 21. Spatial distribution of the first six POD modes at Ma=1.53
图 22 Ma=1.26前3阶POD模态的时间系数演化
Figure 22. Temporal evolution of the first three POD mode coefficients at Ma=1.26
图 23 Ma=1.53前3阶POD模态的时间系数演化
Figure 23. Temporal evolution of the first three POD mode coefficients at Ma=1.53
图 24 Ma=1.26前6阶POD模态频谱特征
Figure 24. Spectral characteristics of the first six POD modes at Ma=1.26
图 25 Ma=1.53前6阶POD模态频谱特征
Figure 25. Spectral characteristics of the first six POD modes at Ma=1.53
图 26 Ma=1.26与Ma=1.53啸音主频的理论计算与实验对比
Figure 26. Theoretical calculation and experimental comparison of screech frequencies at Ma=1.26 and Ma=1.53
图 27 Ma=1.26喷流密度波动与模态1幅值变化对比
Figure 27. Comparison of jet density fluctuation and mode 1 amplitude variation at Ma=1.26
图 28 Ma=1.53喷流密度与模态1幅值的变化
Figure 28. Comparison of jet density fluctuation and mode 1 amplitude variation at Ma=1.53
图 29 Ma = 1.26复模态能量模值分布（上半流场）
Figure 29. Distribution of the energy magnitude of the complex mode at Ma = 1.26 （upper half of the flow field）
图 30 Ma = 1.53复模态能量模值分布（上半流场）
Figure 30. Distribution of the energy magnitude of the complex mode at Ma = 1.53 （upper half of the flow field）
图 31 Ma = 1.26复模态相位结构分布
Figure 31. Phase structure distribution of the complex-valued mode at Ma = 1.26
图 32 Ma = 1.53复模态相位结构分布
Figure 32. Phase structure distribution of the complex-valued mode at Ma = 1.53
图 33 Ma =1.26复模态能量峰值层的相位剖面
Figure 33. Phase profile at the energy peak layer of the complex mode at Ma = 1.26
图 34 Ma =1.53复模态能量峰值层的相位剖面
Figure 34. Phase profile at the energy peak layer of the complex mode at Ma = 1.53
图 35 Ma =1.26扰动声功率与前3阶模态能量变化率的归一化演化对比
Figure 35. Normalized evolution comparison of perturbation acoustic power and the first three modal energy variation rates at Ma =1.26
图 36 Ma=1.53扰动声功率与前3阶模态能量变化率的归一化演化对比
Figure 36. Normalized evolution comparison of perturbation acoustic power and the first three modal energy variation rates at Ma=1.53
图 37 Ma =1.26模态1与模态2、模态3之间的相位差演化
Figure 37. Phase difference evolution between mode 1 and modes 2 and 3 at Ma =1.26
图 38 Ma=1.53模态1与模态2、模态3之间的相位差演化
Figure 38. Phase difference evolution between mode 1 and modes 2 and 3 at Ma=1.53
图 39 Ma =1.26模态1的非线性能量转移项分布
Figure 39. Nonlinear energy transfer distribution of mode 1 at Ma =1.26
图 40 Ma=1.53模态1的非线性能量转移项分布
Figure 40. Nonlinear energy transfer distribution of mode 1 at Ma=1.53
表 1 试验系统参数设置
Table 1. Experimental system parameter settings
参数 设置 Zd（背景平面到流场中心的距离）/mm 1900 Zb（背景平面到相机镜头的距离）/mm 3150 帧率/Hz 10000 分辨率/（像素×像素） 1024 ×1024 快门速度/s 1/ 10000 电子背景点分布范围/（mm×mm） 810× 1070 
下载: 导出CSV
表 2 不同工况下流场总压与总温
Table 2. Total pressure and temperature of the flow field
工况 总压/Pa 总温/K Ma=1.26 252 297 Ma=1.53 356 298
下载: 导出CSV
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