多元可激发气体声弛豫频率的环境影响分析
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摘要
推导多元可激发气体中声弛豫频率和环境温度、压强的解析关系.理论分析和仿真计算表明:声弛豫频率线性反比于主弛豫过程的弛豫时间,正比于主弛豫过程的振动耦合热容,反比于外自由度热容;温度升高导致振动耦合热容增加、内外自由度能量转移速率增大引起弛豫时间减少,进而造成声弛豫频率正比于环境温度;压强增加使得分子碰撞速率增加引起弛豫时间减少,进而使得声弛豫频率线性正比于环境压强.
Analytic relations between acoustic relaxation frequency and external temperature and pressure in multi-component excitable gases are deduced. Theoretical and calculational results show that relaxation frequency is inversely proportional to relaxation time of primary relaxation process, proportional to vibration coupling heat capacity of primary relaxation process, and inversely proportional to external heat capacity. Increase of temperature is related to increase of heat transfer capacity and energy transfer rate of internal and external degrees of freedom, which leads to decrease of relaxation time. It results that relaxation frequency is proportional to ambient temperature. Increase of pressure increases molecular collision rate and causes relaxation time to decrease, which brings about relaxation frequency being linearly proportional to ambient pressure.
Analytic relations between acoustic relaxation frequency and external temperature and pressure in multi-component excitable gases are deduced. Theoretical and calculational results show that relaxation frequency is inversely proportional to relaxation time of primary relaxation process, proportional to vibration coupling heat capacity of primary relaxation process, and inversely proportional to external heat capacity. Increase of temperature is related to increase of heat transfer capacity and energy transfer rate of internal and external degrees of freedom, which leads to decrease of relaxation time. It results that relaxation frequency is proportional to ambient temperature. Increase of pressure increases molecular collision rate and causes relaxation time to decrease, which brings about relaxation frequency being linearly proportional to ambient pressure.
引文
[1] HERZFELD K F, LITOVITZ T A. Absorption and dispersion of ultrasonic waves[M]. New York: Academic, 1959.
[2] LAMBERT J D. Vibrational and rotational relaxation in gases[M]. Oxford: Clarendon, 1977.
[3] BHATIA A B. Ultrasonic absorption [M]. New York: Dover, 1985.
[4] COTTET A, NEUMEIER Y, SCARBOROUGH D, et al. Acoustic absorption measurements for characterization of gas mixing [J]. J Acoust Soc Am, 2004, 116: 2081-2088.
[5] CARLSON J E, CARLSON R. Prediction of molar fractions in two-component gas mixtures using pulse-echo ultrasound and PLS regression [J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2006, 53: 606-613.
[6] PETCULESCU A G. Future trends in acoustic gas monitoring and sensing [J]. Journal of Optoelectronics and Advanced Materials, 2006, 8(1): 217-221.
[7] ZHU M, WANG S, WANG S T, et al. An acoustic gas concentration measurement algorithm for carbon monoxide in mixtures based on molecular multi-relaxation mode [J]. Acta Physica Sinica, 2008, 57(9): 5749-5755.
[8] HU Y, WANG S, ZHU M, ZHANG K S, et al. Acoustic absorption spectral peak location for gas detection [J]. Sens Actuators B: Chem, 2014, 203: 1-8.
[9] ZHANG K S, CHEN L K, OU W H, et al. A theory for monitoring combustion of natural gas based on the maximum point in sound absorption spectrum [J]. Acta Physica Sinica, 2015, 64(5): 054302-1～8.
[10] LIU Y, LIU S, LEI J, et al. An algorithm for multi-physics field reconstruction based on molecular relaxation model of mixtures [J]. Chinese Journal of Computational Physics, 2014, 31(01):67-74.
[11] PETCULESCU A G, LUEPTOW R M. Quantitative acoustic relaxational spectroscopy for real-time monitoring of natural gas: A perspective on its potential [J]. Sensors and Actuators B: Chemical, 2012, 169(1): 121-127.
[12] PETCULESCU A G, HALL B, FRAENZLE R, et al. A prototype acoustic gas sensor based on attenuation [J]. J Acoust Soc Am, 2006, 120(4): 1779-1782.
[13] HU Y, WANG S, ZHU M. A relaxation times coupling method to construct acoustic relaxation calibration for two-frequency measuring gas compositions [J]. Applied Acoustics, 2016, 113: 102–108.
[14] ZHANG K S, WANG S, ZHU M, et al. Analytical model for acoustic multi-relaxation spectrum in gas mixtures[J]. Acta Physica Sinica, 2012, 61(17): 174301-1～11.
[15] ZHANG K S, WANG S, ZHU M, et al. Decoupling multimode vibrational relaxations in multicomponent gas mixtures: Analysis of sound relaxational absorption spectra [J]. Chinese Physics B, 2013, 22(1): 014305-1～10.
[16] ZHU M, LIU T T, WANG S, ZHANG K S. Capturing the molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra [J]. Measurement Science and Technology, 2017, 28(8): 085008-1～9.
[17] KNESER H O. Relaxation processes in gases in physical acoustics Vol II[M]. MASON W P, ed. New York: Academic, 1965: 133-199.
[18] SHIELDS F D. On obtaining transition rates from sound absorption and dispersion curves [J]. J Acoust Soc Am, 1970, 47(5B): 1262-1268.
[19] ZUCKERWAR A J, MEREDITH R W. Acoustical measurements of vibrational relaxation in moist N2 at elevated temperatures [J]. J Acoust Soc Am, 1982, 71(1): 67-73.
[20] ZHANG K S, WANG S, ZHU M, DING Y. Algorithm for capturing primary relaxation processes in excitable gases by two-frequency acoustic measurements [J]. Measurement Science and Technology, 2013, 24(5): 055002-1～8.
[21] LANDAU L, TELLER E. Zurtheorie der schalldispersion[J]. Phys Z Sowjetunion, 1936, 10(1): 34-43.
[22] KNESER H O. The interpretation of the anomalous sound absorption in air and oxygen in terms of molecular collisions [J]. J Acoust Soc Am, 1933, 5(2): 122-126.
[23] SCHWARTZ R N, SLAWSKY Z I, HERZFELD K F. Calculation of vibrational relaxation times in gases [J]. J Chem Phys, 1952, 20(10): 1591-1600.
[24] TANZCOS F. Calculation of vibrational relaxation times of the chloromethanes [J]. J Chem Phys, 1956, 25(3): 439-447.
[25] BAUER H J. SHIELDS F D, BASS H E. Multimode vibrational relaxation in polyatomic molecules [J]. J Chem Phys, 1972, 57(11): 4624-4628.
[26] DAIN Y, LUEPTOW R M. Acoustic attenuation in three-component gas mixtures:Theory [J]. J Acoust Soc Am, 2001, 109(5): 1955-196.
[27] DAIN Y, LUEPTOW R M. Acoustic attenuation in a three-gas mixture: Results [J]. J Acoust Soc Am, 2001, 110(6): 2974-2979.
[28] PETCULESCU A G, LUEPTOW R M. Fine-tuning molecular acoustic models: Sensitivity of the predicted attenuation to the Lennard-Jones parameters [J]. J Acoust Soc Am, 2005, 117(1): 175-184.
[29] ZHANG K S, DING Y, ZHU M, et al. Calculating vibrational mode contributions to sound absorption in excitable gas mixtures by decomposing multi-relaxation absorption spectroscopy [J]. Applied Acoustics, 2017, 116(15): 195-204.
[30] ZHANG K S, ZHU M, TANG W Y, et al. Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements [J]. Acta Physica Sinica, 2016, 65(13): 134302-1～9.
[31] PETCULESCU A G, LUEPTOW R M. Synthesizing primary molecular relaxation processes in excitable gases using a two-frequency reconstructive algorithm [J]. Physical Review Letters, 2005, 94(23): 238301-1～4.
[32] HOLMAN J P. Thermodynamics [M]. New York: McGraw-Hill, 1980.
[33] ZHANG Y, SONG H. Vibration-vibration relaxation of UF6 vibrationally excited molecules [J]. Chinese Journal of Computational Physics, 2014, 31(02):230-236.
[34] WANG R, AN L, SHEN G, et al. Three-dimensional temperature field reconstruction with acoustics based on regularized SVD algorithm [J]. Chinese Journal of Computational Physics, 2015, 32(02):195-201.
[35] EJAKOV S G, PHILLIPS S, DAIN Y, et al. Acoustic attenuation in gas mixtures with nitrogen: Experimental data and calculations [J]. J Acoust Soc Am, 2003, 113(4): 1871-187.
[2] LAMBERT J D. Vibrational and rotational relaxation in gases[M]. Oxford: Clarendon, 1977.
[3] BHATIA A B. Ultrasonic absorption [M]. New York: Dover, 1985.
[4] COTTET A, NEUMEIER Y, SCARBOROUGH D, et al. Acoustic absorption measurements for characterization of gas mixing [J]. J Acoust Soc Am, 2004, 116: 2081-2088.
[5] CARLSON J E, CARLSON R. Prediction of molar fractions in two-component gas mixtures using pulse-echo ultrasound and PLS regression [J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2006, 53: 606-613.
[6] PETCULESCU A G. Future trends in acoustic gas monitoring and sensing [J]. Journal of Optoelectronics and Advanced Materials, 2006, 8(1): 217-221.
[7] ZHU M, WANG S, WANG S T, et al. An acoustic gas concentration measurement algorithm for carbon monoxide in mixtures based on molecular multi-relaxation mode [J]. Acta Physica Sinica, 2008, 57(9): 5749-5755.
[8] HU Y, WANG S, ZHU M, ZHANG K S, et al. Acoustic absorption spectral peak location for gas detection [J]. Sens Actuators B: Chem, 2014, 203: 1-8.
[9] ZHANG K S, CHEN L K, OU W H, et al. A theory for monitoring combustion of natural gas based on the maximum point in sound absorption spectrum [J]. Acta Physica Sinica, 2015, 64(5): 054302-1～8.
[10] LIU Y, LIU S, LEI J, et al. An algorithm for multi-physics field reconstruction based on molecular relaxation model of mixtures [J]. Chinese Journal of Computational Physics, 2014, 31(01):67-74.
[11] PETCULESCU A G, LUEPTOW R M. Quantitative acoustic relaxational spectroscopy for real-time monitoring of natural gas: A perspective on its potential [J]. Sensors and Actuators B: Chemical, 2012, 169(1): 121-127.
[12] PETCULESCU A G, HALL B, FRAENZLE R, et al. A prototype acoustic gas sensor based on attenuation [J]. J Acoust Soc Am, 2006, 120(4): 1779-1782.
[13] HU Y, WANG S, ZHU M. A relaxation times coupling method to construct acoustic relaxation calibration for two-frequency measuring gas compositions [J]. Applied Acoustics, 2016, 113: 102–108.
[14] ZHANG K S, WANG S, ZHU M, et al. Analytical model for acoustic multi-relaxation spectrum in gas mixtures[J]. Acta Physica Sinica, 2012, 61(17): 174301-1～11.
[15] ZHANG K S, WANG S, ZHU M, et al. Decoupling multimode vibrational relaxations in multicomponent gas mixtures: Analysis of sound relaxational absorption spectra [J]. Chinese Physics B, 2013, 22(1): 014305-1～10.
[16] ZHU M, LIU T T, WANG S, ZHANG K S. Capturing the molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra [J]. Measurement Science and Technology, 2017, 28(8): 085008-1～9.
[17] KNESER H O. Relaxation processes in gases in physical acoustics Vol II[M]. MASON W P, ed. New York: Academic, 1965: 133-199.
[18] SHIELDS F D. On obtaining transition rates from sound absorption and dispersion curves [J]. J Acoust Soc Am, 1970, 47(5B): 1262-1268.
[19] ZUCKERWAR A J, MEREDITH R W. Acoustical measurements of vibrational relaxation in moist N2 at elevated temperatures [J]. J Acoust Soc Am, 1982, 71(1): 67-73.
[20] ZHANG K S, WANG S, ZHU M, DING Y. Algorithm for capturing primary relaxation processes in excitable gases by two-frequency acoustic measurements [J]. Measurement Science and Technology, 2013, 24(5): 055002-1～8.
[21] LANDAU L, TELLER E. Zurtheorie der schalldispersion[J]. Phys Z Sowjetunion, 1936, 10(1): 34-43.
[22] KNESER H O. The interpretation of the anomalous sound absorption in air and oxygen in terms of molecular collisions [J]. J Acoust Soc Am, 1933, 5(2): 122-126.
[23] SCHWARTZ R N, SLAWSKY Z I, HERZFELD K F. Calculation of vibrational relaxation times in gases [J]. J Chem Phys, 1952, 20(10): 1591-1600.
[24] TANZCOS F. Calculation of vibrational relaxation times of the chloromethanes [J]. J Chem Phys, 1956, 25(3): 439-447.
[25] BAUER H J. SHIELDS F D, BASS H E. Multimode vibrational relaxation in polyatomic molecules [J]. J Chem Phys, 1972, 57(11): 4624-4628.
[26] DAIN Y, LUEPTOW R M. Acoustic attenuation in three-component gas mixtures:Theory [J]. J Acoust Soc Am, 2001, 109(5): 1955-196.
[27] DAIN Y, LUEPTOW R M. Acoustic attenuation in a three-gas mixture: Results [J]. J Acoust Soc Am, 2001, 110(6): 2974-2979.
[28] PETCULESCU A G, LUEPTOW R M. Fine-tuning molecular acoustic models: Sensitivity of the predicted attenuation to the Lennard-Jones parameters [J]. J Acoust Soc Am, 2005, 117(1): 175-184.
[29] ZHANG K S, DING Y, ZHU M, et al. Calculating vibrational mode contributions to sound absorption in excitable gas mixtures by decomposing multi-relaxation absorption spectroscopy [J]. Applied Acoustics, 2017, 116(15): 195-204.
[30] ZHANG K S, ZHU M, TANG W Y, et al. Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements [J]. Acta Physica Sinica, 2016, 65(13): 134302-1～9.
[31] PETCULESCU A G, LUEPTOW R M. Synthesizing primary molecular relaxation processes in excitable gases using a two-frequency reconstructive algorithm [J]. Physical Review Letters, 2005, 94(23): 238301-1～4.
[32] HOLMAN J P. Thermodynamics [M]. New York: McGraw-Hill, 1980.
[33] ZHANG Y, SONG H. Vibration-vibration relaxation of UF6 vibrationally excited molecules [J]. Chinese Journal of Computational Physics, 2014, 31(02):230-236.
[34] WANG R, AN L, SHEN G, et al. Three-dimensional temperature field reconstruction with acoustics based on regularized SVD algorithm [J]. Chinese Journal of Computational Physics, 2015, 32(02):195-201.
[35] EJAKOV S G, PHILLIPS S, DAIN Y, et al. Acoustic attenuation in gas mixtures with nitrogen: Experimental data and calculations [J]. J Acoust Soc Am, 2003, 113(4): 1871-187.