Investigation of Quantum and Classical Models for Molecular Relaxation Using the Direct Simulation Monte Carlo 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 method, to study acoustics which allows us to simulate real gas effects for all values of Kn with a molecular model that continuum methods cannot offer. Direct simulation Monte Carlo allows us to explore acoustics at varying temperatures, molecular composition, Knudsen numbers, and amplitude. Our current simulations of gas mixtures have employed different methods to model the internal degrees of freedom in molecules and the exchange of translational, rotational and vibrational energies in collisions. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration developed by Borgnakke and Larsen. A second takes into account the discrete 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. In our studies, we have investigated the application of these methods with the direct simulation at the molecular level of the propagation of sound and its attenuation along with their dependence on temperature for diatomic nitrogen systems.