Data assimilation and parameter estimation of thermoacoustic instabilities in a ducted premixed flame

Thermoacoustic instabilities are a persistent challenge in the design of jet and rocket engines. The time-accurate calculation of thermoacoustic instabilities is challenging due to the presence of both aleatoric and epistemic uncertainties, as well as the extreme sensitivity to small changes in certain parameters. Our thermoacoustic system is a vertical Rijke tube containing a premixed Bunsen flame. We conduct experiments and high-fidelity numerical simulations. We then perform data assimilation and parameter estimation using the ensemble Kalman filter to estimate the state and parameters of a simple G-equation model of the flame. Data assimilation provides an optimal estimate of the true state of a system, and improves the predicted shape and location of the flame. Parameter estimation uses the data to find a maximum-likelihood set of parameters for the model while simultaneously quantifying their uncertainty. At the same time, we identify deficiencies in the model with this approach. This process renders the G-equation model quantitatively accurate over the tested range of conditions. As a physics-based model, we expect the G-equation model to extrapolate smoothly. This is going to be tested in future work.