High-enthalpy ionized flows

When an orbital space vehicle enters the Earth's atmosphere, the temperature inside the shock layer is large enough to promote molecular dissociation. Under these conditions the chemical model for air, considered to be formed by N2 (80%) and O2 (20%), includes five species (N2, O2, NO, N, O). It is known that to characterize the flowfield within the shock layer, chemical and thermal non-equilibrium effects must be accounted for, in particular, when kinetic processes (such as dissociation) are enhanced by vibrational excitation. The most conventional and common methodology to tackle this modeling problem is the multi-temperature approach (see chapter 6), which assigns to each molecule an independent vibrational temperature (described by a related continuity equation) which, in turn, affects the chemical rate coefficients. An alternative, the state-to-state approach (see chapters 12 and 13), describing the evolution of the vibrational distributions of the molecular ground electronic state, is being investigated by a growing number of researchers. In the case of super-orbital atmospheric entry, conditions encountered by a space vehicle returning from outer planets or by a meteoroid, the kinetic energy to be dissipated is very large, leading to temperatures which are large enough to cause ionization. At the same time, the electronically excited states of atoms and molecules become relevant in affecting the flow properties and the radiative signature of the plasma in the shock layer. In this context, the state-to-state approach also becomes a fundamental tool to model high-enthalpy flows. At these energies, almost all the molecules are dissociated and the level kinetics of atomic species must be considered. The state-to-state approach for atomic systems is known in the literature as the collisional-radiative model, where the level distribution is determined by the balance among ion recombination, excitation and ionization by electron impact and radiative decay. The computational cost of a collisional-radiative model simulation is typically 1-2 orders of magnitude larger than that required by multi-temperature models. As aresult the use of state-to-state models is not popular among the hypersonic fluiddynamics community, and often remains limited to 0D/1D calculations. To overcome this issue, reduced-order models are being developed, such as coarse-grained models based on energy level grouping, described in section 8.1. Collisional-radiative models often assume a Maxwellian distribution for electron energy, and the related electron temperature is a parameter determining the rate coefficients of electron induced processes such as excitation and ionization. In fluiddynamic calculations, electron temperature is described by an additional continuity equation. However, non-equilibrium electron energy distribution functions (EEDFs) can play an important role in the level and chemical kinetics. The solution of a suitable Boltzmann equation is the answer to this problem. Moreover, the mutual interaction between the level population and EEDF must also be considered, requiring the simultaneous solution of the chemical kinetics and the Boltzmann equation. This approach, known as self-consistent state-to-state kinetics, is described in section 8.2.