Data assimilation using ensemble Kalman filter and low-dimensional manifolds for reacting flow

In this study, an effective and practical algorithm based on the ensemble Kalman filter (EnKF) and low-dimensional manifolds (LDMs) is proposed for the data assimilation of the reacting flow. The EnKF enables better accuracy using observation data, e.g., measurements of temperature and species mass fractions. The LDM is introduced to reduce the number of partial differential equations and increase the computational efficiency. This approach is adopted for solving characteristic problems of unsteady and steady flame, i.e., auto-ignition in a homogeneous reactor and counterflow diffusion flames. Progress variable and mixture fraction are employed for auto-ignition and counterflow diffusion flames, respectively. Results show that ignition delay times are well captured in the prediction of auto-ignition. Effects of uncertainty in the initial conditions are minimized by the assimilation of the temporal evolution of temperature. In the prediction of counterflow diffusion flames, a database is tabulated in the mixture space. Data assimilation is carried out based on measurements of fuel and oxidizer mole fractions and the conserved mixture fraction transport equation. Temperature and species mass fractions are inferred from the pre-tabulated database using the assimilated mixture fraction. It demonstrates that the combination of LDM and data assimilation is able to predict minor species distribution, which is difficult to measure.