Assessment of Vibrational Nonequilibrium for State Resolved Simulation of a Hypersonic Flow

Abstract

Recent developments in internal energy nonequilibrium modeling for hypersonic gas flow simulations indicate a strong need for improved fidelity, and efforts have consequently focused on discrete state kinetic relaxation (DSKR) techniques which independently model quantum state populations. High computational requirements for DSKR modeling of large scale flows have to date limited the applicability of this type of model, and further work is needed to greatly improve model efficiency without compromising accuracy. With an ultimate goal of developing models for DSKR methods with locally adaptive (model) fidelity or other strategies to achieve large efficiency gains, in the present work we investigate various means of quantifying and predicting vibrational nonequilibrium for a representative hypersonic flow. We assess a series of nonequilibrium metrics based on the normalized difference between translational and vibrational temperatures, Kolmogorov-Smirnov (KS) statistics and population ratios which directly measure deviation from equilibrium state populations. Additional metrics are based on time scale ratios that indicate relative magnitudes of collisional equilibration effects and gradient-driven nonequilibrium forcing for individual vibrational states. We consider a simple two-dimensional case of inviscid and N2 flowing over a cylindrical forebody with a freestream Mach number of 6.5. The forced harmonic oscillator model is used to determine rate coefficients for single quantum vibrational-translational energy exchange, while dissociation and vibration-vibration transfer effects are neglected. In observing trends among different nonequilibrium metrics, we find areas of agreement as well as significant discrepancies. These observations point to a need for careful interpretation of nonequilibrium assessments and choice of nonequilibrium metrics in the use of state-to-state kinetics in CFD flow solvers.