Nonlinear Coupled Constitutive Relations for Multi-species Gas Flow with Translational, Rotational and Vibrational Modes

For high-speed and high-temperature flows, various internal energy modes and physicochemical non-equilibrium processes are activated, significantly impacting aerodynamic and aero-heating loads. This paper introduces a nonlinear coupled constitutive relations (NCCR) model of multi-species gases for numerical simulations of hypersonic non-equilibrium flows with translational, rotational and vibrational modes. The model is derived from the modified Boltzmann-Curtiss equations with thermal non-equilibrium, where the rotational relaxation is considered through the bulk viscosity. Meanwhile, the chemical reaction models and Park’s two-temperature model are incorporated to reproduce the real-gas phenomena. An undecomposed algorithm is further extended to the current NCCR model under a finite volume framework for ensuring robust computation. Two numerical tests are utilized to verify the performance of the present solution: hypersonic flows around an experimental sphere and a hypersonic technology vehicle-type flying vehicle. The present model successfully matches wind tunnel experimental data in hypersonic flows against the NCCR model of perfect gases and exhibits superior capability in replicating non-equilibrium phenomena compared to conventional Navier-Stokes equations, particularly in highly non-equilibrium regions, thereby highlighting the engineering potential of the NCCR theory for hypersonic non-equilibrium flows.