Internal Energy Excitation and Dissociation of Molecular Nitrogen in a Compressing Flow

Abstract

Prediction of the radiative heat-flux to the surface of a spacecraft entering a planetary atmosphere strongly depends on the completeness and accuracy of the physical model used to describe the non-equilibrium phenomena in the flow. During an atmospheric entry, the translational energy of the fluid particles drastically rises through a shock. Depending on the intensity of the shock, different physico-chemical processes may take place, such as excitation of the internal energy modes, dissociation of the molecules, ionization of the atoms and molecules. These non-equilibrium phenomena are strongly coupled to each other. For re-entry velocities >10 km/s, a significant portion of the heating experienced by the heat shield can be due to radiation and is highly influenced by the shape of the internal energy distribution function. Understanding thermo-chemical non-equilibrium effects is also important for a correct interpretation of experimental measurements in flight and in ground wind-tunnels. Concentration of the gas species and distribution of their internal energy level populations can be estimated by means of either multi-temperature models (Park 1990) or collisional radiative (CR) models (Laux 2002; Bultel et al. 2006; Magin et al. 2006; Panesi et al. 2009). In multi-temperature models, the physico-chemical properties of the air flow are obtained by assuming that, for all the species, the population of each internal energy mode follows a Boltzmann distribution at its own temperature (Tr rotational, Tv vibrational or Te electronic temperature, respectively). These models have been developed based on experimental data obtained in flight and also in high-enthalpy facilities representative of specific flight conditions, such as in arc-jet and shock-tube wind-tunnels (Appleton et al. 1968). The problem with this approach is that the models may contain many uncertainties that can be extremely difficult to quantify. Moreover, there is no detailed information about the specific state of the gas since these data are highly averaged (e.g., stagnation point heat-flux measurement). Park (2006) has worked extensively on multi-temperature models for air and has also shown that the use of these models, even if very efficient from a computational point of view, can be justified only when the departure from the Boltzmann population is small, i.e., for low-velocity and high-pressure re-entry conditions. Collisional radiative models take into account all relevant collisional and radiative mechanisms between the internal energy levels of the different species in the flow. They constitute a valid alternative to the multi-temperature models since they exhibit a wider range of applicability. By increasing order of complexity and computational time, three kinds of CR models can be distinguished for air: electronic, vibrational and rovibrational. In electronic CR models, transitions between the electronic states are considered and the rovibrational levels of the molecules are populated according to Boltzmann distributions