Second-order constitutive relations and their topologies for rotational non-equilibrium in diatomic gas flows using a multi-temperature approach

Abstract

The phenomenon of rotational relaxation in diatomic gases such as nitrogen was studied in a non-equilibrium flow regime. A higher-order constitutive theory such as the nonlinear coupled constitutive relation (NCCR) approach was used to calculate the flow properties. The bulk viscosity-based approach, employing a single temperature to identify rotational non-equilibrium was found applicable for low Mach number cases. Since diatomic gases are characterized by additional degrees of freedom that may not be in equilibrium with each other in non-equilibrium flows, different temperatures need to be assigned to each degree of freedom to account for the same. Energy exchange between translational and rotational degrees of freedom was accomplished using the rotational energy equation with a non-zero source term. The source term was modeled using the Landau-Teller formulation and involved a rotational collision number representing the average number of collisions required to attain trans-rotational equilibrium. In this work, it was calculated using the simplified formulation proposed by Parker. An additional non-conserved moment equation related to rotational heat flux was formulated under the NCCR framework and was solved in conjunction with other NCCR algebraic equations. It was noticed that the new two-temperature NCCR formulation for rotational non-equilibrium had better agreement with experiments, direct simulation Monte Carlo (DSMC), and molecular dynamics (MD) simulations. Moreover, the formulation was computationally less expensive than the DSMC/MD simulations. A topological analysis was carried out to demonstrate the nonlinearity present in NCCR.