Optimal placement of wall-pressure sensors for data assimilation in high-speed boundary layers

Measurements in hypersonic flows, in particular during flight, are often limited, for example to wall-pressure data at discrete locations. Rather than regard these measurement data as mere records of the wall pressure at the measurement times, data assimilation can predict the entire flow field that satisfies the governing equations and optimally reproduces the measurements (Buchta & Zaki, J. Fluid Mech., 916, A44, 2021). The convergence and accuracy of the assimilation procedure depends on characteristics of the measurements, including the flow quantity being measured, the number of sensors and their placement. In this work, we focus on the impact of sensor position on the accuracy of the data assimilation procedure, and the capacity to accurately estimate high-speed transitional boundary layers. We introduce an algorithm for optimizing the positions of a network of sensors. We then compare the convergence and accuracy of assimilating wall-pressure measurements from the best and worst sensor networks, for an independent flow condition.