Modeling of dissociation and energy transfer in shock-heated nitrogen flows

Abstract

This work addresses the modeling of dissociation and energy transfer processes in shock heated nitrogen flows by means of the maximum entropy linear model and a newly proposed hybrid bin vibrational collisional model. Both models aim at overcoming two of the main limitations of the state of the art non-equilibrium models: (i) the assumption of equilibrium between rotational and translational energy modes of the molecules and (ii) the reliance on the quasi-steady-state distribution for the description of the population of the internal levels. The formulation of the coarse-grained models is based on grouping the energy levels into bins, where the population is assumed to follow a Maxwell-Boltzmann distribution at its own temperature. Different grouping strategies are investigated. Following the maximum entropy principle, the governing equations are obtained by taking the zeroth and first-order moments of the rovibrational master equations. The accuracy of the proposed models is tested against the rovibrational master equation solution for both flow quantities and population distributions. Calculations performed for free-stream velocities ranging from 5 km/s to 10 km/s demonstrate that dissociation can be accurately predicted by using only 2-3 bins. It is also shown that a multi-temperature approach leads to an under-prediction of dissociation, due to the inability of the former to account for the faster excitation of high-lying vibrational states.