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为研究声传播和分子多模式振动能量弛豫的相互关系,本文提出了一种混合气体声 复合弛豫频谱的解析模型.该模型从振动模式微观能量转移及其耦合形成宏观弛豫过程两个角度, 分析了依赖于声频率的混合气体有效热容.并通过求解振动模式能量转移的通用弛豫方程, 最终得到可同时体现主副弛豫过程的声弛豫吸收和声频散的解析结果.仿真结果表明, 对于CO2, CH4, N2和O2组成的多种混合气体, 该模型的声吸收谱与实验数据相符,峰值误差在1%以内,且反映了多振动模式形成的 声复合弛豫吸收谱上通常仅会显现1-2个吸收波峰的物理现象.与已有模型相比, 本解析模型可直接求出混合气体声弛豫频谱上特征点的解析形式,并利于对其进行定性定量分析. 从而为研究声传播特性与气体分子弛豫特性的相互关系提供了一个有效理论模型.To identify the correlation between sound propagation and molecular multimode vibrational relaxation in polyatomic gas mixture, an analytical model that constructs acoustic multi-relaxation spectrum is presented. The frequency-dependent effective specific heat of gas is formulated from the micro view of vibrational mode energy transfer as well as the macro view of relaxation process due to vibrational-vibrational mode energy coupling. With the aid of the general relaxation equations of multimode vibrational energy transfer, the analytical expressions to calculate acoustic relaxation absorption and dispersion, which reflect both primary and secondary relaxation processes, are developed from the effective specific heat. The constructed absorption spectra of various gas mixtures, consisting of carbon dioxide, methane, nitrogen, and oxygen, accord with the experimental data very well. Especially, the peak errors of those results are less than 1%. Moreover, the simulation results illustrate that less than two single processes with higher strength appear generally in a multi-relaxation absorption spectrum. Compared with the existing models, the analytical model can directly obtain the analytical expressions of characteristic points in the relaxation spectrum of gas mixtures, which makes it advantageous to analyze the spectral characteristics qualitatively and quantitatively. Consequently, the model provides an effective approach to analyzing the relationship between sound propagation and molecular vibrational relaxation of gas mixtures.
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Keywords:
- gas relaxation /
- acoustic spectrum /
- acoustic attenuation /
- effective heat capacity
[1] Petculescu A G, Lueptow R M 2007 Icarus 186 413
[2] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[3] Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[4] 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]
[5] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) p55-216
[6] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p1-114
[7] Lueptow R M, Phillips S 1994 Meas. Sci. Technol. 5 1375
[8] Herzfeld K F, Rice F O 1928 phys. rev. 31 691
[9] Knudsen V O 1931 J. Acoust. Soc. Am. 3 126
[10] Bauer H J, Shields F D, Bass H E 1972 J. Chem. Phys. 57 4624
[11] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[12] Tanczos F I 1956 J. Chem. Phys. 25 439
[13] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[14] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[15] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[16] Bass H E, Sutherland L C, Piercy J, Evans L 1984 Absorption of Sound by the Atmosphere in Physical Acoustics edited by Mason W P, Thurston R N (Vol. XVII) (Orlando: Academic) p145-232
[17] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[18] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[19] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[20] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[21] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[22] Zhang H L 2007 Theoretical acoustics (Beijing: Higher Education Press) p221 (in Chinese) [张海澜 2007 理论声学(北京:高等教育出版社) 第221页]
[23] Zhang J C, Yuan P, Ouyang Y H 2010 Acta Phys. Sin. 59 8287 (in Chinese) [张景川, 袁萍, 欧阳玉花 2010 59 8287]
[24] Morse P M, Ingard K U 1968 Theoretical acoustics (New York: McGraw-Hill) p294-300
[25] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324-332
[26] Gravitt J C, Whetstone C N, Lagemann R T 1966 J. Chem. Phys. 44 70
[27] Yardley J T, Moore C B 1968 J. Chem. Phys. 49 1111
[28] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[29] Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
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[1] Petculescu A G, Lueptow R M 2007 Icarus 186 413
[2] Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069
[3] Phillips S, Dain Y, Lueptow R M 2003 Meas. Sci. Technol. 14 70
[4] 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]
[5] Herzfeld K F, Litovitz T A 1959 Absorption and Dispersion of Ultrasonic Waves (New York: Academic) p55-216
[6] Lambert J D 1977 Vibrational and Rotational Relaxation in Gases (Oxford: Clarendon) p1-114
[7] Lueptow R M, Phillips S 1994 Meas. Sci. Technol. 5 1375
[8] Herzfeld K F, Rice F O 1928 phys. rev. 31 691
[9] Knudsen V O 1931 J. Acoust. Soc. Am. 3 126
[10] Bauer H J, Shields F D, Bass H E 1972 J. Chem. Phys. 57 4624
[11] Schwartz R N, Slawsky Z I, Herzfeld K F 1952 J. Chem. Phys. 20 1591
[12] Tanczos F I 1956 J. Chem. Phys. 25 439
[13] Shields F D 1970 J. Acoust. Soc. Am. 47 1262
[14] Evans L B, Bass H E, Sutherland L C 1972 J. Acoust. Soc. Am. 51 1565
[15] Bass H E, Bauer H J, Evans L B 1972 J. Acoust. Soc. Am. 52 821
[16] Bass H E, Sutherland L C, Piercy J, Evans L 1984 Absorption of Sound by the Atmosphere in Physical Acoustics edited by Mason W P, Thurston R N (Vol. XVII) (Orlando: Academic) p145-232
[17] Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012
[18] Dain Y, Lueptow R M 2001 J. Acoust. Soc. Am. 109 1955
[19] Petculescu A G, Lueptow R M 2005 J. Acoust. Soc. Am. 117 175
[20] Ejakov S G, Phillips S, Dain Y, Lueptow R M, Visser J H 2003 J. Acoust. Soc. Am. 113 1871
[21] Petculescu A G, Lueptow R M 2005 Phys. Rev. Lett. 94 238301
[22] Zhang H L 2007 Theoretical acoustics (Beijing: Higher Education Press) p221 (in Chinese) [张海澜 2007 理论声学(北京:高等教育出版社) 第221页]
[23] Zhang J C, Yuan P, Ouyang Y H 2010 Acta Phys. Sin. 59 8287 (in Chinese) [张景川, 袁萍, 欧阳玉花 2010 59 8287]
[24] Morse P M, Ingard K U 1968 Theoretical acoustics (New York: McGraw-Hill) p294-300
[25] Holman J P 1980 Thermodynamics (New York: McGraw-Hill) p324-332
[26] Gravitt J C, Whetstone C N, Lagemann R T 1966 J. Chem. Phys. 44 70
[27] Yardley J T, Moore C B 1968 J. Chem. Phys. 49 1111
[28] Petculescu A G, Hall B, Fraenzle R, Phillips S, Lueptow R M 2006 J. Acoust. Soc. Am. 120 1779
[29] Yan S, Wang S 2008 Acta Phys. Sin. 57 4282 (in Chinese) [鄢舒, 王殊 2008 57 4282]
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