Assimilation of wall-pressure measurements in direct numerical simulations of high-speed flow over a cone–flare geometry

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Abstract
Ensemble-variational (EnVar) assimilation of wall-pressure measurements in direct numerical simulations of Mach 6 flow over a cone–flare is performed. The experimental data include pressure spectra and intensities from seven wall-mounted PCB sensors positioned upstream, within and downstream of the separation region induced by the compression corner. Assimilation of the first two sensors only, all upstream of separation, is insufficient to accurately predict the downstream flow. Assimilating all the sensor data is shown to be essential to correctly predict separation onset and the downstream wall-pressure data. Similar to the experiments, the assimilated flow features intense rope-like structures in the attached region. The simulations additionally predict a localised amplification of disturbances beneath the separation shock, where experimental data are not available. This amplification results from the interaction of the boundary-layer instability modes with the compression shock. The simulations also capture the sharp decrease in wall-pressure intensity across separation, and the amplification of low-frequency three-dimensional disturbances within the recirculation bubble. Additionally, the computations highlight the uncertainty in the post-separation predictions due to the low-frequency unsteadiness of the separation shock. Oscillations of the streamwise velocity modulate the boundary-layer thickness, which in turn introduces variability in disturbance amplification.

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