Reconstructing Dangerous Flow Events Using the Domain of Dependence from Surface Pressure Data

Surface pressure sensors mounted on an airfoil can serve as an effective tool to identify and track dynamic flow events, such as vortex formation and shedding. In this study, we present a pure physics-based framework to reconstruct the likely origin and evolution of dangerous flow structures upstream from sparse surface pressure measurements. Using the adjoint Navier–Stokes equations, we analyze perturbations to the steady laminar flow around a NACA0012 airfoil and characterize the measurement’s domain of dependence via the adjoint operator. Through a duality relation between the forward perturbation field and the adjoint solution, we establish a direct link between surface pressure readings and upstream flow dynamics. The adjoint field, acting as a sensitivity kernel, enables the spatial and temporal localization of coherent structures from sensor data. Our results show that this approach can effectively reconstruct critical flow events in advance, providing a foundation for real-time diagnostics and control in aerodynamic applications.