Data assimilation for state and parameter estimation of partially ionized gases

Partially ionized gases involve complex transport phenomena coupled with volumetric chemical reactions, which are characterized by rate coefficients. We present a data assimilation (DA) framework that combines physics-based models with experimental measurements to estimate state variables and kinetic parameters in these reactive flows. The key challenge lies in inferring rate processes for elastic, inelastic, and ionization collisions from limited observables, particularly when these processes are embedded within advection-dominated transport equations. Two approaches are demonstrated: (1) ensemble Kalman filter (EnKF) applied to a collisional-radiative model using optical emission spectroscopy to infer electron energy distribution functions that govern reaction rates, and (2) extended Kalman filter (EKF) for coupled ion-neutral continuity equations with nonlinear ionization source terms, utilizing laser-induced fluorescence and discharge current data. The EKF implementation addresses numerical challenges through spatially correlated noise and parameter regularization, essential for stable and robust estimation in advective systems. Results show successful reconstruction of spatio-temporal electron temperature profiles that determine ionization rates during 20 kHz breathing oscillations. This framework enables parameter inference for multiscale plasma chemistry (GHz to kHz) within transport-dominated flows, advancing predictive modeling capabilities for engineering systems.