混合气体声复合弛豫频谱的解析模型

Analytical model for acoustic multi-relaxation spectrum in gas mixtures

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.