The influence of separation on the domain of dependence of wall-pressure measurements in high-speed flows

Data assimilation enables the reconstruction of high-speed flows from sparse sensor measurements, such as wall-pressure data. On a cone-flare geometry, accurate prediction of upstream disturbances by assimilation of the wall pressure depends on the observability of the sensors on the cone section, within the separation region induced by the corner-shock, and downstream of reattachment. We introduce the theoretical formulation to evaluate the domain of dependence of wall sensors, with particular focus on the sensitivity to the upstream boundary condition. The results demonstrate the importance of placing sensors both upstream and within the separated flow, to ensure accurate estimation of the upstream unstable Mack modes and the lower frequency modes that become dominant within the separation bubble. We also report an appreciable change in the domain of dependence of sensors downstream of reattachment, which is attributed to the dynamics of the adjoint fields near reattachment and across the corner and reattachment shocks. As such, the low-frequency unsteadiness of this flow, and the associated expansion and retraction of the separation region, can modify the observability of sensors placed near the reattachment line.