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针对具有明显速度梯度的非均匀流场速度分布在线测试难题, 提出了基于多角度投影的激光吸收光谱多普勒速度分布测试方法, 利用多角度投影吸收光谱信息低频能量相对变化对两段式速度分布区间长度与对应速度值进行耦合求解. 建立不同投影角度下吸收光谱平均频偏值与不同速度区间频偏差值之间的函数关系, 提出了基于傅里叶变换的光谱信号低频能量变化分析方法, 解决了不同速度梯度条件下光谱信号微弱变化检测难题. 采用7185.6 cm–1波段H2O特征谱线结合三条投影光路实现了对于两段式速度分布模型的快速重建, 研究了投影角度以及不同幅值噪音对速度分布计算的影响. 分析表明该方法对于具有明显速度梯度的流场中高速区速度值重建结果最佳, 相对误差0.9%, 同时测量噪音对高速区速度值重建结果影响最小. 投影角度增大有利于增强重建方程中不同速度区间光谱频偏差值对速度区间长度比值的灵敏度, 提高测量精度. 考虑到系统测量空间分辨率限制, 0°, 30°, 60°是较为理想的光路分布角度. 研究结果对于推动激光吸收光谱技术在发动机诊断及气体动力学研究中的应用具有重要意义.A novel approach to using tunable diode laser absorption spectrum (TDLAS) is developed for nonuniform velocity distribution measurement by Doppler effect. An analysis of the energy in direct absorption spectrum at low frequencies is made by Fourier transform, because the TDLAS method offers the advantages in using Beer law to deal with coupling relations between velocity distribution and corresponding length of velocity region. By comparing with traditional TDLAS-Doppler velocity measurement, advantages of this approach to the more exact solution of core flow velocity by signal process without using extra lasers and detectors are explored. Following the published theory, between velocity regions at multiple projections the absorbance about average in frequency offsets and the absorbance about difference in frequency offsets are incorporated into an improved fitting model. A solution to obtaining changes of absorbance energy at low frequencies by Fourier transform is used to demonstrate the ability to recover minor change in absorbance under different conditions, inferring a better method to realize the simultaneous measurement of velocity distribution. The influences of these parameters, such as projection angles and noise during absorption, are investigated by the multiple projection simulations at rovibrational transitions of H2O near 7185.6 cm–1 from three projections. This approach is validated in a two-stage velocity distribution model, demonstrating the ability to exactly measure core flow, with a precision of 0.9% RMS (root mean square). The high velocity in the core flow is less influenced by the random noise in absorption due to nearly linear relationship between the difference in frequency offsets and the ratio of length of velocity region. Some satisfied results can be obtained when larger angles of projection are arranged. The combination of 0°, 30°, and 60° will be a reasonable optic design considering the limitation of spatial resolution. In conclusion, the novel approach to velocity distribution measurement based on TDLAS-Doppler from multiple projections has great potential applications in engine diagnosis and gas dynamic research.
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Keywords:
- tunable diode laser absorption spectroscopy /
- Doppler effect /
- Fourier transform /
- velocity distribution
[1] Zhang D, Zhao H, Yang J A 2019 Optik 186 155
Google Scholar
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[3] 杨斌, 齐宗满, 杨荟楠, 黄斌, 刘佩进 2015 燃烧科学与技术 21 516
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图 1 基于多普勒效应的激光吸收光谱测速原理 (a)激光吸收光谱多普勒测速系统示意图; (b)吸收光谱信号多普勒频偏示意图
Fig. 1. TDLAS-based Doppler velocimetry: (a) Diagram of velocity measurement system; (b) diagram of frequency shifts between absorption signals.
图 2 两段式速度分布模型与多光路测试系统示意图 (a)速度分布流场模型示意图; (b)激光吸收光谱速度分布测试系统示意图
Fig. 2. Model and multiple projection system design for two-stage velocity distribution: (a) Velocity distributions assumed in the analysis; (b) illustration of optical system for TDLAS velocity distribution measurement.
图 3 Eθ与Ah/Al和
$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ 的函数关系图Fig. 3. Function diagram of Eθ, Ah/Al and
$\Delta {\nu_{\rm{h} \text{-} l, \theta }}$ .
图 4 不同工况下平均频率偏移计算误差结果
Fig. 4. Relative error of average frequency offset under different conditions.
图 5 60°光路投影条件下
$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ 与Ah/Al的关系 (a)$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ 随Ah/Al的变化; (b)$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ 一阶导数随Ah/Al的变化Fig. 5. Function relationship between
$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ and Ah/Al at 60° optical path: (a)$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ varies with Ah/Al; (b) 1 st derivative of$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ varies with Ah/Al.
图 7 不同Eθ条件下Ah/Al和
$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ 之间函数关系Fig. 7. Relationship between Ah/Al and
$\Delta {\nu_{{{\rm{h}} \text{-}{\rm{l}}}, \theta }}$ at different Eθ.
图 8 不同速度模型条件下投影光路光谱信号特征
Fig. 8. Absorbance features at projection in different velocity models.
表 1 不同角度组合下的计算结果
Table 1. Calculation results under different angle combinations.
投影角度 计算误差 θ1/(°) θ2/(°) Lh/% Vh/% Vl/% 10 20 16.23 7.07 18.92 10 40 15.84 6.88 18.71 10 60 15.84 6.84 18.78 10 80 15.84 6.81 18.84 20 40 15.21 6.58 18.15 20 60 8.74 3.71 12.08 20 80 4.75 2.01 7.35 30 60 2.52 1.07 4.16 30 80 1.74 0.73 2.96 40 60 1.37 0.58 2.36 40 80 1.01 0.42 1.77 
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表 2 不同速度下的计算结果
Table 2. Calculation results at different velocity.
模型流场参数 计算结果相对误差 Vh/m·s–1 Vl/m·s–1 Ah/Al Vh/% Vl/% Lh/% 1000 100 4 0.17 7.47 0.31 1000 100 1 4.74 53.32 14.44 800 300 4 1.60 20.14 4.08 800 300 1 9.56 37.01 17.53 600 300 4 4.32 62.07 19.41 600 300 1 15.15 77.73 36.63
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[1] Zhang D, Zhao H, Yang J A 2019 Optik 186 155
Google Scholar
[2] 张伟, 沈岩, 余西龙, 姚兆普, 王梦, 曾徽, 李飞, 张少华 2015 推进技术 36 651
Zhang W, Shen Y, Yu X L, Yao Z P, Wang M, Zeng H, Li F, Zhang S H 2015 J. Propul. Technol. 36 651
[3] 杨斌, 齐宗满, 杨荟楠, 黄斌, 刘佩进 2015 燃烧科学与技术 21 516
Yang B, Qi Z M, Yang H N, Huang B, Liu P J 2015 J. Combust. Sci. Technol. 21 516
[4] 吕晓静, 李宁, 翁春生 2016 光谱学与光谱分析 36 624
Lv X J, Li N, Weng C S 2016 Spectrosc. Spect. Anal. 36 624
[5] Hanson R K 2011 Proc. Combust. Inst. 33 1
Google Scholar
[6] Li H, Farooq A, Jeffries J B, Hanson R K 2007 Appl. Phys. B 89 407
[7] 洪延姬, 宋俊玲, 饶伟, 王广宇 2018 实验流体力学 32 43
Hong Y J, Song J L, Rao W, Wang G Y 2018 J. Exper. Fluid Mech. 32 43
[8] 刘佩进, 王志新, 杨斌, 魏祥庚 2017 光谱学与光谱分析 37 532
Liu P J, Wang Z X, Yang B, Wei X G 2017 Spectrosc. Spect. Anal. 37 532
[9] 阚瑞峰, 夏晖晖, 许振宇, 姚路, 阮俊, 范雪丽 2018 中国激光 45 1
Kan R F, Xia H H, Xu Z Y, Yao L, Ruan J, Fan X L 2018 Chin. J. Lasers 45 1
[10] 张亮, 刘建国, 阚瑞峰, 刘文清, 张玉钧, 许振宇, 陈军 2012 物理学报 61 034214
Google Scholar
Zhang L, Liu J G, Kan R F, Liu W Q, Zhang Y J, Xu Z Y, Chen J 2012 Acta. Phys. Sin. 61 034214
Google Scholar
[11] Xu Z Y, Kan R F, Ran J, Yao L, Fan X L, Liu J G 2016 Light, Energy Environ Congr. ETu2 A.4
[12] 姚路, 姚德龙, 仪建华, 阚瑞峰, 杨燕京, 许振宇, 阮俊, 刘建国 2016 火炸药学报 39 35
Yao L, Yao D L, Yi J H, Kan R F, Yang Y J, Xu Z Y, Ruan J, Liu J G 2016 Chin. J. Explos. Propellants 39 35
[13] Li F, Yu X L, Cai W W, Ma L 2012 Appl. Opt. 51 4788
Google Scholar
[14] Li F, Yu X L, Gu H B, Li Z, Chen L H, Chang X Y 2011 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference San Francisco, USA, April 11−14, 2011 p2214
[15] Chang L S, Strand C L, Jeffries J B, Hanson R K 2011 AIAA J. 49 2783
[16] Chang L S, Jeffries J B, Hanson R K 2010 AIAA J. 49 2687
[17] Gamba M 2015 53rd AIAA Aerospace Sciences Meeting Kissimmee, USA, January 5−9, 2015 p1222
[18] Qu Q W, Cao Z, Xu L J, Liu C, Chang L Y, McCann H 2019 Appl. Opt. 58 205
Google Scholar
[19] Qu Q W, Gao S, Chang L Y, Xu L J 2019 Appl. Phys. B 125 128
[20] Xiang R, Wang C, Lu L 2019 J. Opt 48 384
Google Scholar
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