Numerical Simulation Of Acoustic Properties Of Multi-component Gas Mixture

The propagation of acoustic waves in gases is intimately linked to gas composition, ambient temperature and gas pressure. This may enable the use of acoustic waves as a quantitative probe of the thermodynamic and molecular properties of gas mixtures, which is the focus of the research of gas sensor. Based on the knowledge of the physical mechanism of sound propagating through a gas, the mathematics models of acoustic propagation are important basics, which could lead to the development of the theory of acoustic gas sensors further. A theoretical predictive model of acoustic attenuation in different gas mixtures is required to determine gas composition based on gas acoustic properties. It has been proved to be necessary for the development of gas composition sensors.Using traditional models of acoustic propagation based on the Navier-Stokes or Euler equations, the gas description is characterized by the temporal and spatial evolution of the gas through partial differential equations. The traditional models assume that deviations from thermal equilibrium in gases are absent or small, and it is the failure of the closure of the Navier-Stokes equations that limit the applications of these models. Typical theoretical predictive models of acoustic attenuation are based on one or several uncertain experiential parameters and need to be improved continually according to new experimental data. And the accuracy of predictive results by these models may rely on the reliability of experimental data. So these models can not meet the requirements of a quantitative analysis of gas properties.In this dissertation, a numerical simulation method for the propagation of acoustic waves in multi-component gas mixture was chosen for the current study. In order to overcome the shortcomings of those traditional theoretical models, an effective theoretical predictive model of acoustic attenuation, which is independent of experiential parameters, was developed. The contribution of this dissertation includes:1. A mathematic model of sound propagating through a gas based on the direct simulation Monte Carlo (DSMC) methodA numerical simulation method was chosen for the study of the propagation of acoustic waves in multi-component gas mixture. And a mathematic model of sound propagating through a gas based on the DSMC method was developed. The DSMC method is a particle approach based on the Boltzmann equation, which includes all physical properties of interest for sound propagation, such as viscous dissipation, attenuation, nonlinear effects, dispersion, nonequilibrium effects, entropy waves, and others. The DSMC method is a model based on the kinetic theory of gas dynamics, which describes gas flows through direct physical modeling of particle motions and collisions. And this method has been proven to converge to the Boltzmann equation in the limit of small time step and small cell size. In fact, the DSMC method is one possible approach which can include essentially all the physics of interest for sound propagation. And this method is necessary for the problems with nonlinear and nonequilibrium effects. Hence, the DSMC method is a very effective way to solve a multi-dimensional complex problem.2. A numerical fitting method of acoustic attenuation spectrum based on the DSMC methodA numerical fitting method of acoustic attenuation spectrum of multi-component gas mixture was proposed. Thus, a predictive model of acoustic attenuation based on the DSMC method was developed, which meets the quantitative requirements of the acoustic attenuation spectra of multi-component gas mixtures by using the numerical simulation method of acoustic propagation based on the DSMC method. Because the predictive model of acoustic attenuation based on the DSMC method describes gas flows through direct physical modeling of particle motions and collisions, the results of the numerical fitting method of acoustic attenuation spectrum include not only the effects of classical and relaxation attenuation, but also the effects of other unfamiliar attenuation. This theoretical predictive model could lead to the development of acoustic gas sensors with high sensitivity based on acoustic attenuation spectra capable of quantitatively determining gas composition.3. A reconstructive algorithm of acoustic relaxation attenuation spectrum with a wide frequency rangeA reconstructive algorithm that synthesizes the relaxation attenuation spectrum in a wide frequency range was developed. And an effective numerical solution of the equation of acoustic relaxation attenuation based on the effective isochoric molecular specific heat was proposed. And the effective relaxation time of gas can be estimated by two approaches, which are base on SSH theory and experimental data respectively. Hence, the relaxation attenuation of polyatomic molecule in gas mixture can be predicted in a wide frequency range. In addition to the advantage of wide frequency range, this reconstructive algorithm consumes low computation time. This algorithm could extend the theoretical predictive model of acoustic attenuation based on the DSMC method to a wide frequency range.This work was supported by the National Natural Science Foundation of China"Gas detection based on acoustic attenuation of multi-frequency ultrasonic"(No. 60472015). In this dissertation, the mathematic model of sound propagating through a gas was developed at microscopic level. Using the reconstructive algorithm of acoustic relaxation attenuation spectrum with a wide frequency range, the attenuation spectra of gas mixtures can be analyzed qualitatively in a wide frequency range, while the effective relaxation frequencies of gas components can be obtained from the trends of the attenuation spectra. Then using the numerical fitting method of acoustic attenuation based on the DSMC method, the attenuation spectra of gas mixtures can be analyzed quantitatively, while some local characteristics of the attenuation spectra can be obtained in detail. Hence, a theoretical predictive framework of acoustic attenuation was developed, which is independent of experiential parameters. This framework could lead to the development of acoustic waves capable for quantitatively probe the thermodynamic and molecular properties of gas mixtures. And the technology of acoustic gas sensors would grow up in the future.