Estimation of electrohydrodynamic force and gas heating fields of plasma actuators using data assimilation

The generation of an electrohydrodynamic (EHD) force and gas heating in surface-barrier discharges supports various applications of plasma actuators (PAs). Understanding the physical location and intensity of the generated EHD force and heating is crucial to assess the aerodynamic and thermal effects of PAs accurately. However, no method exists to measure both fields directly. In this study, we develop a data-assimilation (DA) methodology that combines flow-field measurements and computational fluid dynamics to estimate the EHD force and heating fields inversely from experimental data on transient velocity and density fields. The EHD force and heating fields are represented by Gaussian functions, and the four parameters defining these functions are set as the estimation targets. Numerical experiments successfully demonstrate that the DA methodology can estimate these four parameters using transient flow field data that includes vortex formation. High-accuracy estimation can be achieved even when only the density field is used, whereas DA estimation using only the velocity field cannot estimate the heating field. This difference occurs because the density field is affected by both the EHD force and heating, whereas the velocity field is affected only by the EHD force. A method to determine the initial estimation of the heating field based on a simplified energy conservation equation is proposed and validated, demonstrating the importance of measuring the density field at the very initial stage for high-accuracy DA estimation. The validated DA methodology can also be applied to other discharge phenomena, providing a path toward a better understanding of complex plasma-flow interactions.