Acoustic rotational relaxation of hydrogen around normal temperture

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.