Data assimilation of state-indirect observations for constraining detonation wave dynamics

This study investigates the integration of sparse experimental observations into numerical simulations of detonation waves through data assimilation (DA). We extend a two-step local ensemble transform Kalman filter (LETKF) framework to assimilate numerically generated Schlieren and chemiluminescence images into simulations of a methane–oxygen detonation wave with detailed chemistry. Using an ensemble of 30 simulations, we demonstrate that the method can effectively constrain detonation wave dynamics despite the chaotic and highly nonlinear nature of the complex shock system. Results show that the LETKF reduces errors in unobserved state variables by up to 70%, successfully reconstructing key detonation structures including triple points, Mach stems, and transverse waves. The framework exhibits robustness across multiple assimilation cycles with a 50 kHz observational cadence, maintaining consistent state estimation even as ensemble members naturally diverge. While the method excels at constraining structural features like density and temperature fields, we observe that intermediate species distributions require more frequent observation due to their localized spatial distribution. This work demonstrates the potential of DA techniques for advancing pressure-gain combustion research by enabling the fusion of limited experimental diagnostics with high-fidelity numerical simulations, providing a framework for enhanced understanding of detonation dynamics in practical systems.