Deep learning and variational assimilation of experimental measurements in simulations of hypersonic transition on a cone

Transition to turbulence in high-speed boundary layers is extremely sensitive to the disturbance environment, which is uncertain. As a result, computational studies often focus on canonical transition scenarios and qualitative comparisons to experiments. In contrast, data assimilation can enable us to estimate the uncertain upstream disturbances whose evolution reproduces the available measurements. We will introduce a data assimilation strategy that combines deep learning and ensemble-variational methods to assimilate experimental measurements in high-fidelity simulations. The measurements are wall-pressure spectra acquired from PCB sensors on a 7-degree cone, at free-stream Mach number M=6. We estimate the upstream instability waves, quantitatively reproduce the wall-pressure spectra, and discover the full spatio-temporal flow field that led to the measured data.