Rotational nonequilibrium in state-resolved models for shock-heated flows

Abstract

The effects of molecular rotation on the dynamics of high-temperature nonequilibrium flows is investigated in this work, with an application to nitrogen shocked flows. The overall manifold of rovibrational levels for the ground electronic state of N2 is firstly obtained through the solution of the radial Schrödinger equation over a high-fidelity potential curve. The obtained solutions predict the existence of 9510 states, including quasi-bound states which may spontaneously dissociate through tunneling effects. The lifetimes of such quasi-bound states are determined using a semiclassical method, and most of them are found to be long-lived. A semi-empirical rate for state-specific rotational translations has then been applied so as to examine the importance of rotational dissociation against vibrational dissociation, in equilibrium conditions. Rotational dissociation is found to be one to two orders of magnitude below vibrational dissociation, from low temperatures up to 100,000K. The contribution of quasi-bound states to the overall dissociation rate is also found to be essentially negligible (increase of the rotational dissociation rate by a factor of 1.5–2 in the whole temperature range). Finally, as the full state-specific modeling of the interactions of this large number of rovibrational levels remains out of reach of the state of the art theories and computational resources, a simplified state-specific model for the simulation of shocked flows is proposed, treating vibration-translation and rotation-translation interactions in an uncoupled fashion. A Boltzmann equilibrium distribution is considered for each subset of rotational levels, for each of the molecular vibrational levels, at a characteristic rotational temperature Trotv. Rotational collisional numbers are calculated according to the method recently proposed by Park and confirm the rapid increase of the number of collisions needed for establishing rotational–translational equilibrium, as the gas temperature rises. The results of our simulations also confirm the claims by Park that for high temperatures (roughly above 12,000K), rotational–translational equilibration actually occurs after vibrational-translational equilibration, contrary to the popular belief.