关键词: 弛豫时间/
声弛豫吸收/
弛豫过程/
弛豫频率
English Abstract
Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements
Zhang Ke-Sheng1,Zhu Ming2,
Tang Wen-Yong1,
Ou Wei-Hua3,
Jiang Xue-Qin1
1.School of Information Engineering, Guizhou Institute of Technology, Guiyang 550003, China;
2.School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China;
3.School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550001, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61461008, 61371139 61571201, 61402122), the Natural Science Foundation of Guizhou Province, China (Grant Nos. [2015]2065, [2014]7361), and the Recruitment Program of Guizhou Institute of Technology (Grant No. XJGC20140601).Received Date:20 February 2016
Accepted Date:18 April 2016
Published Online:05 July 2016
Abstract:Vibrational relaxation time is a parameter describing the macroscopic behavior of vibrational energy transition rate between molecular internal degrees of freedom (DOF) and external DOF in excitable gas, which determines the relaxation frequency of the maximum point in acoustic absorption spectrum. To measure the vibrational relaxation time, the traditional methods are used to obtain the acoustic absorption spectra by changing the ambient pressure at several operating frequencies. However, these traditional methods are not suitable for real-time measurement due to the complexity of equipment implementation and the non-ideality of test gas under high pressure. In order to solve those problems, we have developed an algorithm [2013 Meas. Sci. Technol. 24 055002] to capture the primary vibrational relaxation processes only based on the measurements of sound absorption and sound speed at two operating frequencies and a single pressure. But the algorithm only can reconstruct the absorption maximum and it cannot capture the relaxation time with high precision. To measure the frequency dependence of the complex effective specific heat of the relaxing gas, an algorithm synthesizing relaxation processes is given by Petculescu and Lueptow [2005 Phys. Rev. Lett. 94 238301]. In its derivation process, relaxational angular frequency was set to be the inverse ratio to relaxation time. However, the relaxational angular frequency was measured in the adiabatic process of transmission thermodynamic, while the relaxation time was obtained in the thermodynamic isothermal process, the derivation confused the two thermodynamic processes, making the algorithm unable to capture the relaxation frequency with high precision. In order to estimate the relaxation time with higher accuracy, in this paper we first obtain the theoretical relationship among the relaxation times under the three types of thermodynamics conditions, i. e., isothermal, adiabatic constant pressure and adiabatic constant volume. Then we correct the relaxation time derivation and propose our corrected algorithm to reconstruct the relaxation frequencies and relaxation times under the conditions of isothermal, adiabatic constant pressure and adiabatic constant volume. In experiments and simulations, the relaxation times and relaxation frequencies reconstructed by our corrected algorithm for various gas compositions including carbon dioxide, methane, chlorine, nitrogen, and oxygen around room temperature are consistent with the experimental data.
Keywords: relaxation time/
sound relaxational absorption/
relaxation process/
relaxation frequency
