  This work presents a vibrational and electronic state-to-state model for
nitrogen plasma implemented within a multi-physics modular computational
framework to study non-equilibrium effects in inductively coupled plasma (ICP)
discharges. Within the computational framework, the set of vibronic (i.e.,
vibrational and electronic) master equations are solved in a tightly coupled
fashion with the flow governing equations. This tight coupling eliminates the
need for invoking any simplifying assumptions when computing the state of the
plasma, thereby ensuring a higher degree of physical fidelity. To mitigate
computational complexity, a maximum entropy coarse-graining strategy is
deployed, effectively truncating the internal state space. The efficacy of this
reduced StS model is empirically substantiated through zero-dimensional
isochoric simulations. In these simulations, the results obtained from the
reduced-order model are rigorously compared against those obtained from the
full StS model, thereby confirming the accuracy of the reduced StS framework.
The developed Coarse-grained StS model was employed to study the plasma
discharge within the VKI Plasmatron facility. Our results reveal pronounced
discrepancies between the plasma flow fields obtained from StS simulations and
those derived from Local Thermodynamic Equilibrium (LTE) models, which are
conventionally used in the simulation of such facilities. The analysis
demonstrates a substantial departure of the internal state populations of atoms
and molecules from the Boltzmann distribution. These nonequilibrium effects
have important consequences on the energy coupling dynamics, thereby impacting
the overall morphology of the plasma discharge. A deeper analysis of the
results demonstrates that the population distribution is in a
Quasi-Steady-State in the hot plasma core.
