<i>Ab initio</i> based variable hard sphere with vibrational favouring collision model for the direct simulation Monte Carlo study of non-equilibrium flows

The present work focuses on the development of an ab initio collision model, variable hard sphere with vibrational favoring collision model (VHSV), developed from collision cross sections obtained from the quasi-classical trajectory method for the direct simulation Monte Carlo (DSMC) method. The ab initio collision model includes the effect of the vibrational quantum level of the molecular gases in the calculation of the collision cross section, which is generally absent in the traditional DSMC collision models. The role of vibrational quantum levels on the collision cross section can further affect the physics of inelastic energy exchange and reactive collisions, especially in the shock structure, which has a high degree of non-equilibrium. The method employs a fitting polynomial using the moving average method for estimating the collision cross section for atom–molecule and molecule–molecule collisions. The VHSV model is implemented in the in-house DSMC code to simulate a wide range of problems that include micro-Couette flow with non-equilibrium boundary conditions, shock structure for nitrogen at frozen conditions, and hypersonic reacting molecular oxygen gas flow over a cylinder at a high Mach number. The results from the simulations employing the VHSV and ab initio chemistry models are compared with those obtained using the traditional variable hard sphere collision model (VHS) and the total collision energy chemistry model. The ab initio model simulated results show higher values of velocity slip and temperature jumps in contrast with those estimated by the VHS results in the case of micro-Couette flow. For the cases of steady shock structure and hypersonic flow over cylinder simulations, the peak translational, rotational, and vibrational temperatures obtained from the VHSV model results are higher than those of the VHS model results. The ab initio-based VHSV collision model can be seen as an improved version of the traditional collision models, which is expected to accurately estimate collision cross sections at higher degrees of non-equilibrium and at high temperatures with minimal computational overhead.