常温下氢气声转动弛豫模型研究

张向群; 王殊; 朱明

doi:10.7498/aps.67.20172665

摘要

氢气声弛豫过程主要由氢气分子的转动弛豫决定.然而，当前大部分声弛豫模型是基于气体分子的振动弛豫，并不适用于氢气.本文利用理想气体焓变与定压热容的关系，提出了一种基于氢气分子转动的弛豫模型，并讨论了转动弛豫和振动弛豫的相似与不同.该模型不仅适用于氢气，还能够和其他气体的振动弛豫模型相结合求解混合气体的声弛豫吸收谱和声速频谱.仿真结果表明，对于H2，N2/H2，CO2/H2等气体，该模型生成的声速、声弛豫谱曲线与实验数据符合.本模型为包含氢气的混合气体声学探测提供了一个有效的理论模型.

关键词:

Abstract

Hydrogen is an important energy carrier, and it is widely used due to its extraordinary advantages, such as high heat, clean fuel, being large-scale and renewable. The detection of hydrogen is essential in practical application. Therefore, many researches have focused on monitoring the hydrogen concentration over the past years. Acoustic relaxation theory based on molecular relaxation process is a very promising method of detecting hydrogen gas. However, the existing acoustic relaxation models for gas detection are developed from the vibrational relaxation of gas molecules, and thus they are not applicable for hydrogen and its mixture. In this paper, we present a model for the rotational relaxation process of hydrogen. Firstly, the molecular relaxation process of hydrogen is different from those of other gases due to its large spacing of rotational energy-level and special molecular physical structure. Acoustic relaxation process of hydrogen is mostly determined by the molecular rotational relaxation. Hydrogen molecule is made up of one quarter of para-hydrogen and three quarters of ortho-hydrogen at normal temperature. There is three-rotational-level model for hydrogen rotational relaxation, such as rotational level in states with J=0, 2, 4 (J is rotational quantum-number) for para-hydrogen and J=1, 3, 5 for ortho-hydrogen. Secondly, we introduce effective specific heat into one-mode rotational relaxation at constant pressure, and then extend it to multi-mode rotational relaxation. Upon periodic perturbation of acoustic waves, the temperature and the number of molecules in each rotational level change periodically in the relaxation process. On the basis, we obtain the relaxation equations in a matrix form and calculate effective specific heat at constant pressure for rotational relaxation process. With the relationship between the complex wave number and the effective thermodynamics acoustic speed, we calculate the frequency-dependent acoustic speed and relaxation absorption, and then discuss the difference between the rotational relaxation and the vibrational relaxation. Thirdly, we compare the predicted acoustic speed and absorption spectrum with their corresponding experimental data and investigate the influences of rotational characteristics on absorption spectra in hydrogen and its mixtures. The simulation results show that acoustic speed and relaxation absorption curves calculated by the proposed model are in good agreement with their corresponding experimental data. The model is not only applicable to pure hydrogen gas but also can be used to obtain the acoustic relaxation spectra of gas mixtures with multiple vibrational modes. This model provides a theoretical foundation for the acoustic detecting of hydrogen gas mixtures.

Keywords:

acoustic relaxation /
rotational relaxation /
gas detection /
effective specific heat at constant pressure

作者及机构信息

1.
华中科技大学电子信息与通信学院, 武汉 430074;

2.
许昌学院信息工程学院, 许昌 461000

通信作者: 朱明, zhuming@mail.hust.edu.cn

基金项目: 国家自然科学基金（批准号：61571201，61371139，61461008）、河南省高等学校重点科研项目计划（批准号：15A510037）和河南省高校科技创新人才计划（批准号：18HASTIT022）资助的课题.

Authors and contacts

1.
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China;

2.
School of Information Engineering, Xuchang University, Xuchang 461000, China

Corresponding author: Zhu Ming, zhuming@mail.hust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61571201, 61371139, 61461008), the Program for Key Scientific Research in Universities of Henan Province, China (Grant No. 15A510037), and the Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 18HASTIT022).

参考文献

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[2]	Hanf S, Bgzi T, Keiner R, Frosch T, Popp J 2015 Anal. Chem. 87 982
[3]	Hbert T, Boon-Brett L, Black G, Banach U 2011 Sens. Actuators B: Chem. 157 329
[4]	Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
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[8]	Du G, Zhu Z M, Gong X 2012 Acoustics Foundation (Nanjing: Nanjing University Press) pp295-310
[9]	Liu T, Wang S, Zhu M 2017 J. Acoust. Soc. Am. 141 1844
[10]	Hong J, Lee S, Seo J, Pyo S, Kim J, Lee T 2015 ACS Appl. Mater. Interfaces 7 3554
[11]	Minami Y, Yogi T, Sakai K 2011 J. Opt. 13 075708
[12]	Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[13]	Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[14]	Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
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[18]	Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[19]	Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
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[21]	Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[22]	Hu Y, Wang S, Zhu M, Zhang K S, Liu T, Xu D 2014 Sens. Actuators B: Chem. 203 1
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[24]	Zhu M, Liu T, Wang S 2017 Meas. Sci. Technol. 28 085008
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[27]	Geide K 1963 Acta Acust. Acust. 13 31
[28]	Sluijter C G, Knaap H F P, Beenakker J J M 1964 Physica 30 745
[29]	Knaap H F P, Sluijter C G, Beenakker J J M 1965 Lw Temp. Phys. 1 1233
[30]	Winter T G, Hill G L 1967 J. Acoust. Soc. Am. 42 848
[31]	Behnen S W, Rothwell H L, Amme R C 1971 Chem. Phys. Lett. 8 318
[32]	Bauer H J, Bass H E 1972 J. Chem. Phys. 57 1763
[33]	Davison W D 1964 Proc. Roy. Soc. Ser. A 280 227
[34]	Montero S, Prez-Ros J 2014 J. Chem. Phys. 141 114301
[35]	Sears F W, Salinger G L 1976 Thermodynamics, Kinetic Theory and Statistical Thermodynamics (3rd Ed.) (Reading, Massachusetts: Addison_Wesley Pub. Co.) pp413-415
[36]	Li W 1989 Thermodynamics and Statistical Physics (Beijing: Beijing Institute of Technology Press) pp89- 120 (in Chinese) [李卫 1989 热力学与统计物理 (北京: 北京理工大学出版社) 第89120页]
[37]	Valley L M, Amme R C 1968 J. Acoust. Soc. Am. 44 1144
[38]	Minami Y, Yogi T, Sakai K 2009 J. Appl. Phys. 106 113519
[39]	Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) pp115-129
[40]	Herzfeld K F, Litovitz T H 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) pp338-343
[41]	Stewart E S, Stewart J L, Hubbard J C 1945 Phys. Rev. 68 231
[42]	Raff L M, Winter T G 1968 J. Chem. Phys. 48 3992
[43]	Bhatia A B 1985 Ultrasonic Absorption (New York: Dover) pp87-101
[44]	Warren P M 1964 Physical Acoustics: Principles and Methods (Vol. 2) (London: Academic Press) pp160-180
[45]	Wan J K S, Ioffe M S, Depew M C 1996 Sens. Actuators. B: Chem. 32 233

施引文献

[1]	Melaina M W, Antonia O, Penev M 2013Blending Hydrogen Into Natural Gas Pipeline Networks: a Review of Key Issues (Golden, CO: National Renewable Energy Lab.) Report No. NREL/TP-5600-51995
[2]	Hanf S, Bgzi T, Keiner R, Frosch T, Popp J 2015 Anal. Chem. 87 982
[3]	Hbert T, Boon-Brett L, Black G, Banach U 2011 Sens. Actuators B: Chem. 157 329
[4]	Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[5]	Zhang K S, Zhang X Q, Tang W Y, Xiao Y Q, Jiang X Q 2018 Acta Acust. 43 399 (in Chinese) [张克声, 张向群, 唐文勇, 肖迎群, 蒋学勤 2018 声学学报 43 399]
[6]	Hauptmann P, Hoppe N, Pttmer A 2002 Meas. Sci. Technol. 13 R73
[7]	Hu J H, Zheng X F 2011 Practical Infrared Spectroscopy (Beijing: Science Press) pp1-20 (in Chinese) [胡皆汉, 郑学仿 2011 实用红外光谱学 (北京: 科学出版社) 第120页]
[8]	Du G, Zhu Z M, Gong X 2012 Acoustics Foundation (Nanjing: Nanjing University Press) pp295-310
[9]	Liu T, Wang S, Zhu M 2017 J. Acoust. Soc. Am. 141 1844
[10]	Hong J, Lee S, Seo J, Pyo S, Kim J, Lee T 2015 ACS Appl. Mater. Interfaces 7 3554
[11]	Minami Y, Yogi T, Sakai K 2011 J. Opt. 13 075708
[12]	Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[13]	Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[14]	Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[15]	Petculescu A G, Lueptow R M 2012 Sens. Actuators B: Chem. 169 121
[16]	Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
[17]	Jia Y Q, Wang S, Zhu M, Zhang K S, Yuan F G 2012 Acta Phys. Sin. 61 095101 (in Chinese) [贾雅琼, 王殊, 朱明, 张克声, 袁飞阁 2012 61 095101]
[18]	Zhang K S, Wang S, Zhu M, Hu Y, Jia Y Q 2012 Acta Phys. Sin. 61 174301 (in Chinese) [张克声, 王殊, 朱明, 胡佚, 贾雅琼 2012 61 174301]
[19]	Zhang K S, Chen L K, Ou W H, Jiang X Q, Long F 2015 Acta Phys. Sin. 64 054302 (in Chinese) [张克声, 陈刘奎, 欧卫华, 蒋学勤, 龙飞 2015 64 054302]
[20]	Zhang K S, Zhu M, Tang W Y, Ou W H, Jiang X Q 2016 Acta Phys. Sin. 65 134302 (in Chinese) [张克声, 朱明, 唐文勇, 欧卫华, 蒋学勤 2016 65 134302]
[21]	Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[22]	Hu Y, Wang S, Zhu M, Zhang K S, Liu T, Xu D 2014 Sens. Actuators B: Chem. 203 1
[23]	Zhu M, Wang S, Wang S T, Xia D H 2008 Acta Phys. Sin. 57 5749 (in Chinese) [朱明, 王殊, 王菽韬, 夏东海 2008 57 5749]
[24]	Zhu M, Liu T, Wang S 2017 Meas. Sci. Technol. 28 085008
[25]	Rhodes Jr J E 1946 Phys. Rev. 70 932
[26]	Takayanagi K, Kishimoto T 1953 Prog. Theor. Phys. 9 578
[27]	Geide K 1963 Acta Acust. Acust. 13 31
[28]	Sluijter C G, Knaap H F P, Beenakker J J M 1964 Physica 30 745
[29]	Knaap H F P, Sluijter C G, Beenakker J J M 1965 Lw Temp. Phys. 1 1233
[30]	Winter T G, Hill G L 1967 J. Acoust. Soc. Am. 42 848
[31]	Behnen S W, Rothwell H L, Amme R C 1971 Chem. Phys. Lett. 8 318
[32]	Bauer H J, Bass H E 1972 J. Chem. Phys. 57 1763
[33]	Davison W D 1964 Proc. Roy. Soc. Ser. A 280 227
[34]	Montero S, Prez-Ros J 2014 J. Chem. Phys. 141 114301
[35]	Sears F W, Salinger G L 1976 Thermodynamics, Kinetic Theory and Statistical Thermodynamics (3rd Ed.) (Reading, Massachusetts: Addison_Wesley Pub. Co.) pp413-415
[36]	Li W 1989 Thermodynamics and Statistical Physics (Beijing: Beijing Institute of Technology Press) pp89- 120 (in Chinese) [李卫 1989 热力学与统计物理 (北京: 北京理工大学出版社) 第89120页]
[37]	Valley L M, Amme R C 1968 J. Acoust. Soc. Am. 44 1144
[38]	Minami Y, Yogi T, Sakai K 2009 J. Appl. Phys. 106 113519
[39]	Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) pp115-129
[40]	Herzfeld K F, Litovitz T H 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) pp338-343
[41]	Stewart E S, Stewart J L, Hubbard J C 1945 Phys. Rev. 68 231
[42]	Raff L M, Winter T G 1968 J. Chem. Phys. 48 3992
[43]	Bhatia A B 1985 Ultrasonic Absorption (New York: Dover) pp87-101
[44]	Warren P M 1964 Physical Acoustics: Principles and Methods (Vol. 2) (London: Academic Press) pp160-180
[45]	Wan J K S, Ioffe M S, Depew M C 1996 Sens. Actuators. B: Chem. 32 233

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