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高超声速飞行器在临近空间飞行时, 由于飞行器与空气剧烈的相互作用, 形成包含等离子体鞘套和尾迹的等离子体流场, 研究其电子密度分布特性对高超声速飞行器的目标识别、测控通信等具有重要意义. 地面模拟实验测量是研究等离子体包覆高超声速飞行器电磁散射特性的有效方法之一, 为满足地面模拟实验瞬态等离子体流场电子密度分布的测量需求, 本文提出了一种Ka波段七通道微波干涉仪测量系统研制方案. 该系统采用单发七收的方式, 利用单曲面透镜将波导开口天线辐射的电磁波转化为近似平面波, 将7个平行且非对称排列的开口波导作为接收通道天线, 缩减了接收天线的尺寸以及天线之间的距离, 提高了测量的空间分辨率. 基于七通道微波干涉仪测量系统在弹道靶和激波管设备开展了动态实验, 测量了超高速流场电子密度二维分布, 结果表明该系统具备瞬时大动态范围信号的接收能力, 幅度线性动态范围优于65 dB, 相位动态范围180°, 响应时间优于1 μs; 所测量的超高速流场等离子体电子密度二维分布, 能够较好地反映弹道靶设备与激波管设备产生的瞬态等离子体细节变化, 电子密度测量动态范围为(1010—1013)cm–3量级, 电子密度测量误差不超过0.5个数量级, 径向空间分辨率优于15 mm.When a hypersonic vehicle is flying in the near space region, the strong friction between the vehicle and the air can cause the air to ionize. As a result, the plasma sheath around the vehicle and the wake flow field behind it are formed, significantly affecting the electromagnetic (EM) scattering characteristics of the vehicle and resulting in the communication blackout. Therefore, the investigation of electron density distribution of the plasma sheath and wake flow field is of the great significance in the detection, communication, etc. of the hypersonic target. In order to meet the requirements for on-ground electron density distribution measurement of the transient plasma flow fields, the feasibility of measuring electron density profile with seven-channel microwave interferometer measurement system is demonstrated in this work. The wake plasma is modeled as a non-uniform multilayer medium, and the full-wave simulation software FEKO is used to calculate the phase-shift information of EM wave transmitting through non-uniform single-layered dielectric plate, uniform and non-uniform multi-layered dielectric plates. According to the simulation results, the dielectric constant of the substrate is retrieved and compared with the preset result. The retrieved results show that it is feasible that the dielectric constant distribution of non-uniform multi-layered dielectric plate is measured by utilizing the proposed microwave interferometer system with one transmission port and seven receptions. The amplitude-phase dynamic range analysis of the proposed Ka-band microwave measurement system is also carried out. The key technologies including large instantaneous amplitude-phase dynamic range and ray tracking inversion algorithm for two-dimensional (2-D) electron density distribution are also developed. Finally, the complete scheme of Ka-band seven-channel microwave interferometer measurement system is introduced. The system includes one lens antenna to generate the required plane wave and seven open-ended waveguide receiving antennas which are asymmetrically arranged to improve the lateral spatial resolution of the system. The system exhibits the amplitude dynamic range and the phase dynamic range of over 65dB and 180° under 1 MHz IF bandwidth respectively. The plasma electron density distributions are measured by utilizing the proposed seven-channel microwave interferometer system in the ballistic range and multi-functional shock tube. The response time of the system is smaller than 1μs, satisfying the requirement for the two-dimensional distribution measurement of the transient plasma flow field generated by the ballistic range and multi-functional shock tube. The differences between experimental and numerical results are less than 0.5 order of magnitude, and the variations in transient plasma generated in both ballistic target and shock tube equipments are well detected. The measurement range of plasma electron density is 1010－1013 cm–3 and the spatial resolution is better than 15mm. In addition, the proposed ray tracing method is also used to invert the two-dimensional(2D) electron density distributions of both square layered model and cylindrical layered model under identical experimental state. The results are in consistent with each other, indicating that the proposed ray tracing method can be used in the inversion of 2D electron density distribution of plasma with different shapes.
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Keywords:
- hypervelocity flow field /
- plasma /
- microwave interferometer /
- electron density /
- distribution measurement
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图 2 七通道微波干涉仪测量示意图
Fig. 2. Schematic of seven-channel microwave interferometer measurement.
图 4 七通道微波干涉法测试分区域介质板仿真结构图
Fig. 4. Simulation of multi-channel microwave interferometry with non-uniform dielectric plate.
图 5 近场扫描与开口波导天线接收相位结果反推分区域介质板的介电常数对比图
Fig. 5. Comparison of dielectric constant distributions of the dielectric plate achieved with near-field scanning and open waveguide antenna.
图 6 分层介质板平面波激励近场扫描仿真结构示意图
Fig. 6. Schematic of plane wave incident on uniform multi-layered dielectric plate.
图 7 开口波导天线接收相位结果反推分区域介质板的介电常数与理论值对比图
Fig. 7. Comparison between the theoretical dielectric constant and that deduced from the phase information results received by open waveguide antennas.
图 8 分层分区域介质平板仿真结构示意图
Fig. 8. Simulation model of non-uniform multi-layered dielectric plate.
图 9 分层分区域介质板介电常数仿真结果与理论值对比图
Fig. 9. Comparison between simulation and theoretical results of the dielectric constant of non-uniform multi-layered dielectric plate.
图 10 七通道Ka波段微波干涉仪测量系统工作原理图
Fig. 10. Schematic of the seven-channel Ka-band microwave interferometer measurement system.
图 11 宽度100 mm的空间分布接收天线阵示意图(尺寸单位: mm)
Fig. 11. Diagram of the receiving antenna array with a width of 100 mm(The dimensions in the figure are in mm).
图 12 Al2O3球模型尾迹处电子密度径向二维分布 (a) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 10ϕ; (b) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 50ϕ; (c) ϕ15 mm Al2O3球, P = 20 kPa, V = 4.80 km/s, x = 100ϕ
Fig. 12. Two-dimensional radial electron density distribution of plasma wake generated by spherical Al2O3 models: (a) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 10ϕ; (b) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 50ϕ; (c) ϕ15 mm Al2O3 ball, P = 20 kPa, V = 4.80 km/s, x = 100ϕ.
图 13 Al2O3球超高速等离子体流场驻点线上各化学反应的组元生成率曲线图 (a) $ {{\text{O}}_{2}} + {{\text{M}}_{1}} \Leftrightarrow {\text{2 O + }}{{\text{M}}_{1}} $; (b) $ {{\text{N}}_{2}} + {{\text{M}}_{2}} \Leftrightarrow {\text{2 N + }}{{\text{M}}_{2}} $; (c) $ {\text{NO}} + {{\text{M}}_{3}} \Leftrightarrow {\text{N + O + }}{{\text{M}}_{3}} $; (d) $ {\text{NO}} + {\text{O}} \Leftrightarrow {{\text{O}}_{2}}{\text{ + N}} $; (e) $ {{\text{N}}_{2}} + {\text{O}} \Leftrightarrow {\text{NO + N}} $; (f) $ {\text{N}} + {\text{O}} \Leftrightarrow {\text{N}}{{\text{O}}^{+}}{+}{{\text{e}}^{\text{ - }}} $
Fig. 13. Reaction rates vs. distance along wall from stagnation point of plasma flow field of supersonic spherical Al2O3 model: (a) $ {{\text{O}}_{2}} + {{\text{M}}_{1}} \Leftrightarrow {\text{2 O + }}{{\text{M}}_{1}} $; (b) $ {{\text{N}}_{2}} + {{\text{M}}_{2}} \Leftrightarrow {\text{2 N + }}{{\text{M}}_{2}} $; (c) $ {\text{NO}} + {{\text{M}}_{3}} \Leftrightarrow {\text{N + O + }}{{\text{M}}_{3}} $; (d) $ {\text{NO}} + {\text{O}} \Leftrightarrow {{\text{O}}_{2}}{\text{ + N}} $; (e) $ {{\text{N}}_{2}} + {\text{O}} \Leftrightarrow {\text{NO + N}} $; (f) $ {\text{N}} + {\text{O}} \Leftrightarrow {\text{N}}{{\text{O}}^{+}}{+}{{\text{e}}^{\text{ - }}} $.
图 15 激波管等离子体电子密度不同反演方法对比图 (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s
Fig. 15. Comparison of plasma electron density in shock tube achieved with various methods: (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s.
图 16 激波管等离子体不同分层模型反演结果对比 (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s
Fig. 16. Comparison of inversion results of shock tube plasma achieved with various models: (a) P = 30 Pa, V = 5.00 km/s; (b) P = 150 Pa, V = 5.55 km/s.
表 1 PMMA实测测试结果
Table 1. PMMA test results.
工作频率/
GHz$ {\varepsilon _{\text{r}}} $ $ \Delta {\varepsilon _{\text{r}}} $/% 开口波导法 微波干涉仪法 8.0 2.73 2.84 3.87 8.5 2.87 2.76 3.99 9.0 2.60 2.71 4.06 9.5 2.57 2.65 3.01 10.0 2.58 2.62 1.53 10.5 2.58 2.59 0.39 11.0 2.52 2.56 1.56 11.5 2.45 2.52 2.78 12.0 2.47 2.49 0.80 
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表 2 在工作频率为35 GHz下理想等离子体层电子密度测试范围
Table 2. Electron density test range of plasma at 35 GHz.
碰撞频率/GHz 等离子体厚度/cm 等离子体密度下限/(1010 cm–3) 等离子体密度上限/(1010 cm–3) 5 1 306.2 1120.1 2 162.2 612.1 8 42.27 163.5 20 16.98 64.5 40 8.511 32.4 60 5.072 22.1 10 1 171.4 1121.3 2 88.31 653.5 8 22.49 173.1 20 9.036 70.0 40 4.529 35.3 60 3.02 23.5
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