Reduction of State-to-State to Macroscopic Models for Hypersonics

Abstract

Four different types of macroscopic models developed for the vibration-chemistry coupling in nonequilibrium flows for re-entry applications are presented. First, using an approach based on nonequilibrium thermodynamics, global rate coefficients of dissociation of N 2 and O 2 under parent molecular or atomic impact and backward molecular recombination are determined. Then a Two-Level Distribution (TLD) model is developed, in which a relaxation equation for vibrational temperature is solved as in the case of multi-temperature models but with the simultaneous solution of a kinetic equation, as in the case of state-to-state models, but only for the last vibrational level. In a third approach, a multiinternal temperature model is presented to describe accurately the vibrational distribution function in using several groups of levels, within which the levels are assumed to follow a Boltzmann distribution at an internal temperature of the group. This multi-internal temperature model allows us to describe accurately the vibrational energy relaxation and dissociation processes behind a strong shock wave. Finally, a rovibrational collisional coarse-grain model is developed to reduce a detailed rovibrational mechanism for the internal energy excitation and dissociation processes behind a strong shock wave in a nitrogen flow.

Vibrational and electronic collisional-radiative model in air for Earth entry problems

“…The resulting rate coefficients have been expressed under the form of a modified Arrhenius law [see Eq. (6)] and implemented in our model. Table II summarizes the processes and reactions considered in CoRaM-AIR.…”

“…(12), an interpolation under the modified Arrhenius form (6) has been performed. Table III lists the related parameters for transitions involving the electronic ground state.…”

“…The resulting underpopulation with respect to equilibrium has been already observed. 6,37 The behavior of the NO vibrational states departs from the one of N 2 and O 2 . The Zel'dovich processes (20) and (21) lead to a rapid population of almost all vibrational levels.…”

“…It is interesting to note that previous studies have proved that the ratio between the forward and backward global rate coefficients departs from the corresponding equilibrium constant when temperature increases. 5,6 Distinguishing different groups of states characterized by a partial equilibrium can then be useful. 6 Unfortunately, these macroscopic models are no longer relevant when the flow significantly departs from equilibrium.…”

“…5,6 Distinguishing different groups of states characterized by a partial equilibrium can then be useful. 6 Unfortunately, these macroscopic models are no longer relevant when the flow significantly departs from equilibrium. Direct state-to-state approaches have to be developed, especially in the dissociation region where the vibrational distribution is not Boltzmanian.…”