Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

Abstract

A multi-degree-of-freedom (MDOF) kinetic model is developed to simulate three-dimensional nonequilibrium flows. By modifying collision term of Boltzmann model equation, a multi-scale molecular collision mechanism with translational, rotational and vibrational degrees of freedom is indicated by three coupled relaxation processes. Molecular vibration is modeled by harmonic oscillator. As a result, the degree of freedom of vibration may be directly related to temperature. Internal energy of various degrees of freedom are computed based on the equipartition theorem, and equilibrium distribution functions for each relaxation step are calculated. The present MDOF kinetic model is beneficial for assessing multi-scale evolutions of internal energy and molecular inelastic collisions. Several three-dimensional flow cases, including lid-driven cavity flow and hypersonic flows around a blunt cone at varying angles of attack, are simulated using the current MDOF technique. All numerical results were consistent with the reference data. It was shown that the proposed MDOF kinetic model well explains the vibration–rotation-translation energy exchange of polyatomic molecules in high-temperature gas, and that the current computational technique is a useful engineering tool for nonequilibrium aerodynamic research.