Investigation of Quantum and Classical Models for Molecular Relaxation Using the Direct Simulation Monte Carlo (dsmc) Method

It is widely known that losses due to viscous, thermal and molecular relaxation play an important role in sound propagation. Traditionally, acoustics is concerned with the treatment of the fluid as a (linear) continuum using macroscopic quantities such as velocity and pressure as dependent variables. However, the continuum model has its limitations and the model breaks down for Knudsen numbers (Kn) greater than roughly 0.05, where Kn is defined as the ratio of mean free path to wavelength. Particle or Boltzmann equation methods are necessary for, but not limited to, problems with Kn > 0.05. In our studies we have used a particle method, Bird’s direct simulation Monte Carlo (DSMC) method, for the direct physical modeling of particle motions and intermolecular collisions in several acoustics problems. Using DSMC to study acoustics allows us to explore real gas effects for all values of Kn with a molecular model that continuum methods cannot offer. DSMC allows us to explore acoustics at varying temperatures, molecular composition, Knudsen numbers, and amplitude. In our current DSMC calculations for gas mixtures we have explored different methods to simulate the internal degrees of freedom in molecules and the exchange of translational, rotational and vibrational energies in collisions of molecules. One of these is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration developed by Borgnakke and Larson. A second takes into account the discrete ICSV14 • 9–12 July 2007 • Cairns • Australia quantum energy levels for vibration with rotation treated classically. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. A third method considers individual quantum vibrational-rotational levels. In our studies we have investigated the application of these methods in the direct simulation at the molecular level of the propagation of sound and its attenuation along with their dependence on temperature for several gas mixtures.