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Photoacoustic spectroscopy (PAS) offers intrinsic attractive features in the detection of trace gases, including ultra-compact size and background-free absolute absorption measurement. The photoacoustic (PA) cell is a key component in the PAS system, which determines the performance of the PAS sensor. In this paper, a cylindrical resonant photoacoustic cell is taken as a research target. Based on the fundamental theory of acoustics and absorption spectrum, a mathematical model of acoustic field excitation in the PA cell is established. The acoustic resonance frequency, quality factor and cell constant of the PA cell are used as three key parameters to describe its performance. By employing advanced computer numerical calculation and finite element simulation technology, we establish a simulation model and impose the excitation load and boundary conditions on the model according to the actual working conditions. Then we calculate and simulate the acoustic modal of the PA cell, and the first eight acoustic modal values of the cavity and the visual vibration model of the acoustic pressure are obtained. With considering the acoustic loss, the thermo-acoustic coupling multi-physical field simulation of photoacoustic cell is carried out. Comparing with analytical calculation and experiment results, the reliability and feasibility of using numerical simulation method to calculate the relevant parameters of photoacoustic cell are demonstrated. In order to obtain a better structure of photoacoustic cell, an optimization algorithm combining response surface proxy model with multi-objective genetic algorithm is proposed. We try to change the shapes of both ends of the resonator in the original photoacoustic cell into the shape of the bell mouth. Take into account the case that the longitudinal acoustic normalization frequency of the PA cell is larger than 1000 Hz, Pareto optimal solution set with the maximum quality factor Q and cell constant Ccell of the PA cell is obtained. The results show that the maximum error between the predicted and simulated values of the proxy model of the PA cell Q and Ccell is only 1.3%. Comparing with the original PA cell, the Q factor and the Ccell of the optimized PA cell are increased by 48.9% and 34.4%, respectively. The performance of the optimized photoacoustic cell is obviously improved. The proposed algorithm of photoacoustic numerical simulation combined with multi-objective optimization design can provide helpful reference for designing the PA cell in PAS sensor development.
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Keywords:
- optics /
- photoacoustic spectroscopy /
- photoacoustic cell /
- numerical calculation
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Shi Q, Hu S M 1998 Chin. J. Chem. Phys. 1 20 (in Chinese)
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Rosencwaig A (translated by Wang Y J, Zhang S Y, Lu Z G) 1986 Photoacoustics and Photoacoustic Spectroscopy (Beijing: Science Press) p35 (in Chinese)
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图 1 光声光谱气体检测原理示意图
Figure 1. Schematic diagram of photoacoustic spectroscopy gas detection principle.
图 2 光声光谱气体检测实验装置图
Figure 2. Photoacoustic spectroscopy gas detection device.
图 3 光声池空腔声学物理模型
Figure 3. Acoustic physical model of photoacoustic cell cavity.
图 4 光声池空腔声学模态仿真云图
Figure 4. Acoustic mode simulation of photoacoustic cell cavity: (a)The first mode (265 Hz); (b) the second mode (1659 Hz); (c) the third mode (3125 Hz); (d) the fourth mode (3490 Hz); (e) the fifth mode (3680 Hz); (f) the sixth mode (4966 Hz) ; (g) the seventh mode (5123 Hz); (h) the eighth mode (6207 Hz).
图 5 光声池二维轴对称物理模型
Figure 5. Two dimensional axisymmetric physical model of photoacoustic cell.
图 6 谐振腔中部混合网格剖分细节图
Figure 6. Detail drawing of mixed meshes in the middle of resonator.
图 7 光声池粗频响应仿真曲线
Figure 7. Simulation curve of photoacoustic cell's coarse frequency response.
图 8 光声池细频响应仿真曲线
Figure 8. Simulation curve of photoacoustic cell's fine frequency response.
图 9 光声池谐振腔母线声压特性曲线
Figure 9. Sound pressure characteristic curve of cavity geometry of photoacoustic cell.
图 10 光声池谐振腔轴线正交中心线温升特性曲线
Figure 10. Temperature rise characteristic curve of orthogonal center line of photoacoustic cavity resonator axis.
图 11 计算结果比较
Figure 11. Comparison of calculation results: (a) Resonance frequency; (b) quality factor; (c) pool constant; (d) boundary layer thickness.
图 12 光声池参数优化设计选取
Figure 12. Optimum design parameters of photoacoustic cell.
图 13 Pareto最优解前沿分布图
Figure 13. Pareto optimal solution frontier distribution map.
表 1 因素水平表
Table 1. The factors and levels graph.
因素 编码水平 –1 0 1 A: 底圆半径rc/mm 5 6 7 B: 圆台高度hc/mm 8 10 12 C: 谐振腔半径Rc/mm 3 4 5 D: 谐振腔长度Lc/mm 60 70 80 
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表 2 代理模型拟合结果
Table 2. Fitting results of surrogate models.
目标响应 相关系数R2 校正系数R2adj P值 f1(x): Q 0.9997 0.9993 < 0.0001 f2(x): Ccell/(Pa·cm) · W–1 0.9999 0.9982 < 0.0001 f3(x): f/Hz 0.9998 0.9996 < 0.0001
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表 3 优化后设计变量值
Table 3. Optimized scheme value.
方案 rc/mm hc/mm Rc/mm Lc/mm 1 5.96 11.99 3.55 61.43 2 5.6 11.99 4.78 60.28 3 7.0 11.99 5.0 60.0 4 5.6 12.0 4.7 60.0
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表 4 相关指标结果对比
Table 4. Comparison of index results.
指标 初始值 优化后 变化率/% 代理
模型数值
模拟误差
率/%Q 63.7 95.2 94.9 0.32 + 48.9 Ccell/( Pa·cm) ·W–1 1750 2321 2353 1.3 + 34.4 f/Hz 1648 2000 2002 0.1 + 21.4
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[1] Webber M E, MacDonald T, Pushkarsky M B, Patel C K N, Zhao Y J, Marcillac N, Mitloehner F M 2005 Meas. Sci. Technol. 16 1547
Google Scholar
[2] Sicilianid C M, Viciani S, Borri S, Patimisco P, Sampaolo A, Scamarcio G, Natale P D, D'Amato F, Spagnolo V 2014 Opt. Express 22 28222
Google Scholar
[3] Hussain A, Petersen W, Staley J, Hondebrink E, Steenbergen W 2016 Opt. Lett. 41 1720
Google Scholar
[4] Yin X K, Dong L, Wu H P, Zheng H D, Ma W G, Zhang L, Yin W B, Xiao L T, Jia S T, Tittel F K 2017 Opt. Express 25 32581
Google Scholar
[5] Thaler K M, Berger C, Leix C, Drewes J, Niessner R, Haisch C 2017 Anal Chem. 89 3795
Google Scholar
[6] Kreuzer L B 1971 J. Appl. Phys. 42 2934
Google Scholar
[7] Besson J P, Schilt S, Thévenaz L 2004 Spectrochim. Acta A: Mol. Biomol. Spectrosc. 60 3449
Google Scholar
[8] Tavakoli M, Tavakolib A, Taheri M, Saghafifar H 2010 Opt. Laser Technol. 42 828
Google Scholar
[9] Pernau H F, Schmitt K, Huber J 2007 Eurosensors 168 1325
Google Scholar
[10] Baumann B, Kost B, Wolff M, Knickrehm S 2007 Comsol. Conference Grenoble, France, 2007 p1.
[11] 陈伟根, 刘冰洁, 胡金星, 周恒逸, 李剑 2011 重庆大学学报 34 7
Google Scholar
Chen W G, Liu B J, Hu J X, Zhou H Y, Li J 2011 J. Chongqing Univ. 34 7
Google Scholar
[12] 周彧, 曹渊, 朱公栋, 刘锟, 谈图, 王利军, 高晓明 2018 物理学报 67 084201
Google Scholar
Zhou Y, Cao Y, Zhu G D, Liu K, Tan T, Wang L J, Gao X M 2018 Acta Phys. Sin. 67 084201
Google Scholar
[13] Liu K, Mei J X, Zhang W J, Chen W D, Gao X M 2017 Sens. Actuat. B: Cheml. 251 632
Google Scholar
[14] 彭勇, 于清旭 2009 光谱学与光谱分析 29 2030
Google Scholar
Peng Y, Yu Q X 2009 Spectrosc. Spect. Anal. 29 2030
Google Scholar
[15] Wu H P, Dong L, Zheng H D, Yu Y J, Ma W G, Zhang L, Yin W B, Xiao L T, Jia S T, Tittel F K 2017 Nat. Commun. 8 15331
Google Scholar
[16] 马欲飞, 何应, 于欣, 于光, 张静波, 孙锐 2016 物理学报 65 060701
Google Scholar
Ma Y F, He Y, Yu X, Yu G, Zhang J B, Sun R 2016 Acta Phys. Sin. 65 060701
Google Scholar
[17] 史强, 胡水明 1998 化学物理学报 1 20
Shi Q, Hu S M 1998 Chin. J. Chem. Phys. 1 20 (in Chinese)
[18] 罗森威格A. 著(王耀俊, 张淑仪, 卢宗桂 译) 1986 光声学和光声谱学(北京: 科学出版社)第35页
Rosencwaig A (translated by Wang Y J, Zhang S Y, Lu Z G) 1986 Photoacoustics and Photoacoustic Spectroscopy (Beijing: Science Press) p35 (in Chinese)
[19] 周鋐, 侯维玲, 吴孟乔 2012 中国工程机械学报 10 463
Google Scholar
Zhou H, Hou W L, Wu M Q 2012 Chin. J. Const. Mach. 10 463
Google Scholar
[20] Kost B, Baumann B, Germer M, Wolff M, Rosenkranz M 2011 Appl. Phys. B 102 87
Google Scholar
[21] 胡俊峰, 徐贵阳, 郝亚洲 2015 光学精密工程 23 1096
Google Scholar
Hu J F, Xu G Y, Hao Y Z 2015 Opt. Precis Eng. 23 1096
Google Scholar
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