Data assimilation in high-speed flow over a cone-flare at Mach 6

Incident disturbances in high-speed boundary layers are often probed by a limited number of wall-pressure sensors. Flow separation has a dramatic impact on the sensitivity of these sensors to the disturbance field, especially when sensors are placed within separation. This sensitivity ultimately determines the capacity to estimate the flow from measurements. We perform data assimilation in a cone-flare configuration at free-stream Mach number M=6, using an ensemble-variational (EnVar) approach (Buchta et al, J. Fluid Mech., 947, R2, 2022). Starting from a few, isolated pressure probes, we determine the upstream disturbance that reproduced the measurements. We discuss the impact of separation on the forward evolution of the instability waves and the dual problem of state estimation. As expected, sensors within separation, downstream of the compression wave, have degraded sensitivity to second-mode waves. However, they remain essential for accurate prediction of the trans-separation region, and for reproducing the experimental measurements. The results provide a first-of-its-kind interpretation of wall-pressure measurements on a cone-flare at high Mach number.